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Algorithmic Feature Highlighting for Human--AI Decision-Making
\blfootnote{ Yifan Guo ([email removed]) and Jann Spiess ([email removed]), Graduate School of Business, Stanford University. We thank Haozhan Gao and three anonymous referees for helpful comments. }
In high-stakes decision-making, algorithms frequently assist rather than replace human decision-makers. For example, algorithms may screen resumes, but final hiring decisions are still made by managers. In such settings, having algorithms recommend a final action may not be sufficient for decision-makers to make high-quality decisions that reflect their private information and preferences. Instead, effective algorithmic support tools should surface interpretable and verifiable details that are most relevant to the final decision.
In this article, we propose a model of joint human--algorithm decision-making in which the algorithm highlights key features that are relevant to the downstream decision of the human decision-maker. We model highlighting as a constrained information policy that selects which of a large number of features to reveal. We show that simple and computationally tractable algorithms are able to improve markedly over policies that instead always reveal the same features, and that this gain is robust to different ways in which decision-makers may interpret the selected features. Overall, we argue that highlighting presents a practically appealing and computationally feasible tool for achieving human--algorithm complementarity that raises rich theoretical questions and warrants further investigation.
We model human--algorithm interaction as a principal--agent game between an algorithm designer (principal) who decides which features to highlight and a human decision-maker (agent) who observes the highlighted features and makes a decision. The joint goal of principal and agent is to choose an action for a decision instance that is characterized by a potentially high-dimensional feature vector. The algorithm designer specifies an algorithm that observes the full feature vector and selects a subset of its components to report to a bandwidth-constrained decision-maker. The human decision-maker observes only those features highlighted by the algorithm. After receiving the highlighted features, the agent infers missing information and then chooses an action. For example, when a candidate applies for a job, the algorithm may observe all information contained in the application and then strategically highlight a subset of features for the human HR manager, who makes the final decision. Throughout, we assume that preferences between the algorithm designer and the decision-maker are aligned.
We believe that our focus on highlighting features rather than providing predictions or summaries has two important advantages in practice: First, presenting more than a simple prediction or recommended action allows the human decision-maker to learn richer information that provides important context and can be combined with private information. Second, the constraint that the algorithm can only pick existing features means that the provided information is interpretable, trustworthy, and verifiable. For example, simply providing a summary generated by large-language models (LLMs) could be problematic since we cannot generally guarantee that it contains only factual information about a given case. By contrast, even if we use an LLM to decide which features to highlight, the resulting information remains correct by construction, even without strong guarantees about the underlying algorithm. \footnote{This would still leave space for deception by a misaligned principal since the choice of which features are selected could be driven by a different objective kamenica2011bayesian, but the deception would then mainly be driven by failing to highlight the most relevant information rather than misrepresenting feature values.}
We consider different modes of human decision-making to highlight potential limitations in practice. We focus on two benchmark models of human decision-makers: a sophisticated agent and a naive agent. Both agents observe the features highlighted by the algorithm and update their posteriors accordingly. The sophisticated agent also takes into account the information contained in the algorithm's decision about which features to highlight, in addition to the value of the highlighted features. By contrast, the naive agent ignores why the algorithm highlights specific features and processes only the highlighted features at face value. For example, a hiring manager could be sophisticated if they respond not just to the information contained in a summary, but also to what is left out. Or they could be naive if they simply fill in the blanks based on their best guess, without taking into account why some information may be included or left out. In practice, a real decision-maker may behave as a mixture of these two types, exhibiting both sophisticated and naive behaviors.
We show that these different modes of updating have vastly different implications for optimal highlighting policies, their robustness, and their computation. We first document gaps between the optimal policies for naive and sophisticated agents, and the cost of optimizing for one when the audience is the other. While the sophisticated agent always does at least as well as the naive agent, we show in simple examples that deploying a policy that targets the naive agent may still lead to an arbitrarily large gap from the optimal policy for a sophisticated audience (“price of simplicity”). Conversely, we demonstrate that a highlighting policy optimized for a sophisticated agent can have arbitrarily bad performance for a naive agent (“price of complexity”) relative to the latter's optimal policy. Beyond the potential cost to naive agents, we illustrate that optimal sophisticated solutions tend to be overly complex.
Optimal solutions that optimize for a sophisticated decision-maker not only lack robustness; they are also often infeasible to compute. Since the sophisticated agent interprets not only the revealed features, but also takes into account why they were revealed, the principal's optimization problem should account for this additional information channel. As with hardness results in algorithmic Bayesian persuasion, we show that the optimal highlighting problem for a sophisticated agent is NP-hard. Therefore, aiming for first-best highlighting schemes for sophisticated decision-makers may lead to overly complex and unintuitive solutions that are both computationally intractable and lack robustness against suboptimal agent decisions.
In contrast to the sophisticated case, even first-best optimal solutions for naive updating can generally be computed in polynomial time. Beyond such first-best solutions, we also consider even simpler greedy solutions that select features based on the incremental information they provide. Focusing on the case of independent binary features, we show that this greedy solution yields first-best outcomes for the naive agent and provides additional gains for the sophisticated agent. Specifically, we provide an analytical characterization of the asymptotic average loss for both types of agents, which we extend to the case where there may be limited correlation across features.
We show that the simple algorithms we consider can substantially outperform a benchmark in which a fixed set of features is highlighted. By highlighting ex-post surprises, we can generally obtain considerably smaller losses across both sophisticated and naive updaters. We show that these algorithms have some surprising properties. For example, in our setting, it is not generally optimal to always highlight the maximal allowable number of features, since additional information does not always lead to better downstream decisions. Instead, optimal algorithms may withhold incremental information if that information misleads more than it helps.
We illustrate these findings in a calibrated numerical exercise using data from the American Housing Survey. Using data from around 1,500 homes from the Minneapolis--St. Paul metro area and a Gaussian belief model over 44 housing characteristics, we show that contextual highlighting policies improve substantially over fixed policies: for example, when highlighting up to $k=10$ features, a contextual greedy algorithm cuts loss by more than half. The exercise also confirms the non-monotonicity result in practice: a contextual greedy policy with ten features outperforms even full revelation of all 43 non-price features. Overall, the exercise demonstrates how a relatively simple, computationally efficient greedy algorithm can produce highly informative posteriors even when updating is naive.
The assumptions of perfect alignment, joint priors, and (partially) rational updating represent substantive limitations of our main model, which suggest important further work. We therefore also discuss extensions to more realistic updating rules and additional frictions between principal and agent. Beyond sophisticated and naive agents, we consider specific behavioral biases in which agents update their beliefs based on stereotypes. We also discuss private information of the agent, wrong beliefs, and misaligned preferences. In addition to these extensions, we discuss more complex feature distributions. With Normally distributed features, we show that sophisticated solutions take unintuitive and complex forms, reinforcing our prescription to optimize for naive updating.
The remaining article is structured as follows. (ref) reviews the related literature in human--AI interaction, information design, and feature revelation. (ref) introduces the model of algorithmic feature highlighting with naive and sophisticated updating. (ref) characterizes the cost of misoptimization when the designer targets the wrong updating type. (ref) studies computational complexity, establishing hardness for sophisticated updating and tractability for naive updating, and analyzes greedy algorithms. (ref) provides closed-form optimal policies and asymptotic loss characterizations for independent binary features. (ref) presents our simulation study based on the American Housing Survey. (ref) discusses extensions, and (ref) concludes.
We contribute to an interdisciplinary literature that aims to model and develop solutions for human--algorithm interaction. We also build upon approaches from information design and the literature on subset selection under constraints.
We relate to a growing literature that studies how humans and algorithms jointly make decisions. noti2025ai formalizes AI-assisted decision making with a learning human and shows that the optimal feature-revelation schedule balances short-run accuracy against long-run human learning, yielding a tractable combinatorial characterization. greenwood2025designing analyzes instance-contingent algorithmic delegation; it shows that the optimal delegate can be strictly better than the best standalone AI and provides both hardness results and efficient algorithms. tan2026should studies the complementary question of when to dispatch a human reviewer under a budget on human effort, deriving a closed-form optimal rule and applying it to AI-assisted peer review. athey2020allocation studies the allocation of decision authority between humans and AI. boyaci2024human studies how machine input affects accuracy and effort, while green2019principles articulates practical principles for algorithm-in-the-loop decision making. balakrishnan2025human shows that feature transparency reduces naive advice-weighting bias in human--algorithm collaboration with private information. More broadly, work on designing human--AI collaboration under behavioral responses agarwal2025designing,mclaughlin2022algorithmic studies how optimal disclosure, recommendation, and automation designs change when humans exhibit biased responses. bastani2026improving studies sequential decision-making and proposes an RL-based approach to produce simple, interpretable “tips” targeted to bottlenecks in the human policy. mclaughlin2024designing,hoong2025improving provide frameworks for algorithmic recommendations that allow for suboptimal responses. Our framework differs in that the AI never acts or makes recommendations directly; instead, it strategically selects which features to surface, and we characterize how performance depends on whether the human anticipates (or neglects) the policy dependence of revealed information.
A closely related strand uses decision theory to characterize the value of information that one agent can contribute to another's decision. guo2025value formalizes human--AI complementarity through the expected improvement in best-attainable payoff from an additional signal, and guo2026complllm operationalizes this idea by fine-tuning an LLM to extract signals from a supervisor's context that complement an existing agent's recommendation. These works take the space of signals as exogenously given and assume that the receiver best-responds to the induced posterior. By contrast, our signals arise endogenously as a subset of the underlying feature vector, which ensures that the revealed content is interpretable and verifiable by construction. vaccaro2024when conducts a meta-analysis of 106 studies, finding that human--AI combinations on average perform worse than the best of humans or AI alone. angelova2023algorithmic documents that many judges underperform when overriding algorithmic recommendations. alur2024human proposes a framework for incorporating human expertise by distinguishing algorithmically indistinguishable inputs. donahue2022human provides theoretical conditions under which complementarity is achievable or impossible.
Our revelation policy can be viewed as a signaling scheme, directly connecting our setting to the literature on information design and Bayesian persuasion. The foundational work of kamenica2011bayesian introduced Bayesian persuasion, formalizing how a sender commits to an information structure to influence a receiver's action; a closely related precursor, rayo2010optimal, characterizes optimal disclosure by a sender who commits ex ante to a signal structure and shows that optimal disclosure generically pools states into coarse partitions. This framework has since been extended across economics and operations research: candogan2020information surveys applications in operations, and dughmi2016algorithmic develops algorithmic tools for computing persuasion schemes with complexity guarantees.
We adopt this information-design perspective but introduce behavioral heterogeneity by modeling the receiver as either naive (ignoring the selection event) or sophisticated (conditioning on the revelation rule), and we derive structural and computational results for optimal revelation under both types. Relatedly, yu2023encoding combines information design with behavioral modeling via deep learning, demonstrating how to incorporate empirically estimated human responses into signaling schemes. In contrast, we focus on an analytically tractable model of belief formation (naive vs.\ sophisticated) and provide explicit guarantees. The closest work to ours is hoefer2024algorithmic, which studies algorithmic persuasion with constraints on the design space imposed by verifiable evidence. Their model allows the sender to choose among evidentiary messages subject to a feasibility constraint, whereas in our setting, the highlighted information must correspond to a subset of the state's features. Related work on privately informed receivers, including guo2019interval, characterizes the sender-optimal disclosure policy as an interval structure, providing a tight structural benchmark for persuasion when the receiver holds private information.
Our model is closely related to the broad literature on subset selection under a cardinality constraint. In our setting, the most direct benchmark is fixed subset selection: the algorithm commits ex ante to a single set of features to highlight and uses the same set for every instance. This benchmark parallels classical feature selection and sparse approximation problems, where the goal is to select a small number of coordinates that best predict an outcome or reconstruct the remaining coordinates. Such problems are often computationally challenging in the worst case, motivating approximation algorithms and structural conditions under which greedy methods are effective. In the context of selecting predictive variables, das2011submodular analyzes greedy subset selection for regression-type objectives via spectral conditions and the submodularity ratio, providing guarantees even when exact submodularity does not hold. Relatedly, observation and feature-acquisition objectives in probabilistic models are often approximately submodular, yielding principled greedy policies krause2007near. However, our setting focuses on instance-wise feature selection, which can strictly outperform the fixed-subset benchmark.
We model the interaction between an algorithm that highlights features and a bandwidth-constrained human decision-maker who updates their belief and takes actions based on the highlighted features. We assume that a decision instance is given by a random vector $X = (X_i)_{i \in M} \sim \mathbb{P}$ with a finite index set $M$ of size $|M| = d$. \footnote{In (ref) we discuss extensions to human private information, in which case features are given by $X = (X_M,X_H)$ with machine features $X_M$ and human features $X_H$.}
\paragraph{Highlighting policy.} We model feature highlighting as follows. We assume that the features $X = (X_i)_{i \in M} \in \mathcal{X}$ are accessible to an algorithm that selects (or “highlights”) a subset $I \subseteq M$ with $|I| \leq k$ and reveals the set $I$ as well as the associated features $X_I = (X_i)_{i \in I}$ to the human decision-maker. Here, $k$ is an exogenously given bandwidth constraint that limits the number of features that can be highlighted. A (deterministic) highlighting policy is a map $$ \sigma: \mathcal{X} \to \{I \subseteq M: |I|\le k\}. $$ Randomized policies can be modeled similarly; deterministic policies suffice for our main hardness and separation results. We assume that this highlighting policy is chosen by an algorithm designer, who acts as the principal of our game.
Here, the highlighting policy can be interpreted as follows. In hiring, a company may use an algorithm to assist HR in the recruiting process; the algorithm highlights several key features in each applicant's resume. In a hospital, the algorithm may highlight key components of a patient's medical file to assist doctors in their final assessment. In school admissions, the algorithm may highlight key aspects of each candidate's background for the admissions committee.
\paragraph{Human belief formation.} Upon observing $(I, X_I)$, the human decision-maker forms a posterior belief over the unknown components of $X$. We assume that the human decision-maker knows the distribution $\mathbb{P}$ (which acts as their prior), and consider two main ways in which the decision-maker updates to form a posterior:
Here, we assume for simplicity that updating is based on the true distribution $\mathbb{P}$. However, our model directly extends to the case where updating is performed according to some prior $\widetilde{\mathbb{P}}$ that may or may not be equal to $\mathbb{P}$. In that case, we can still write $\widehat{\mathbb{P}}^S$ and $\widehat{\mathbb{P}}^N$ for the corresponding posteriors.
\paragraph{Decision and loss.} After forming a belief $\widehat{\mathbb{P}}(\cdot \mid I, X_I)$, the human chooses an action $a \in A$ to minimize expected loss. Given a loss function $\ell: A \times \mathcal{X} \to \mathbb{R}$, the human plays a Bayes action $$ \widehat a(\ell, \widehat{\mathbb{P}}) \in \qopname\relax n{argmin}_{a\in A} \mathbb{E}_{\widehat{\mathbb{P}}}[\ell(a,X)]. $$ The loss at instance $X$ is then $ L(\widehat{\mathbb{P}}, X) \;=\; \ell\!\bigl(\widehat a(\ell,\widehat{\mathbb{P}}), X\bigr). $
\paragraph{Design objective.} We focus on aligned objectives: the algorithm designer seeks to minimize expected loss according to the same loss function. For agent type $\tau\in\{S,N\}$ and policy $\sigma$, define the expected loss (risk) as $$ R^\tau(\sigma) ~:=~ \mathbb{E}\Bigl[ L\bigl(\widehat{\mathbb{P}}^{\tau}(\cdot \mid I, X_I),\, X\bigr) \Bigr], \qquad I=\sigma(X). $$ The design problem is $$ \qopname\relax n{min}_{\sigma:\,|\,\sigma(x)\,|\le k} \; R^\tau(\sigma). $$ If the designer faces uncertainty over human types, a natural Bayesian objective is a weighted average $\lambda R^S(\sigma)+(1-\lambda)R^N(\sigma)$ for some population share $\lambda\in[0,1]$. A robust alternative is to minimize the worst-case loss across types, $\qopname\relax n{min}_{\sigma:\,|\,\sigma(x)\,|\le k} \qopname\relax n{max}\{R^S(\sigma),R^N(\sigma)\}$. In settings where sophisticated updating weakly improves performance relative to naive updating for every policy, this minimax problem reduces to minimizing naive risk.
\paragraph{Special case: recovery.} A common special case is recovery of a target quantity $y=y(x)\in\mathbb{R}^m$. Let $A=\mathbb{R}^m$ and define squared loss $$ \ell(a,x) = \|a-y(x)\|_2^2. $$ Then $\widehat a(\ell,\widehat{\mathbb{P}})=\mathbb{E}_{\widehat{\mathbb{P}}}[y(X)]$ is the posterior mean.
\paragraph{Robust microfoundation for squared loss.} The squared loss above admits a robust interpretation when the downstream decision problem is not known to the algorithm designer. Suppose the human's action $a\in\mathbb{R}^m$ feeds into a downstream task whose payoff depends on an unknown linear combination $\beta^\top a$ of the reported action, evaluated against the target $\beta^\top y(x)$ under quadratic loss $(\beta^\top(a-y(x)))^2$. If the coefficient $\beta\in\mathbb{R}^m$ is unknown and may be chosen adversarially from the unit ball $\{\beta:\|\beta\|_2\le 1\}$, the worst-case loss reduces to $$ \sup_{\|\beta\|_2\le 1}\;\bigl(\beta^\top(a-y(x))\bigr)^2 \;=\; \|a-y(x)\|_2^2, $$ which is exactly the squared loss above.
\paragraph{Special case: outcome-targeted recovery.} In our simulations, we consider a specific loss function that combines full recovery of the feature vector with prediction loss for a specific target. In this case, $y(x) =
$ for some target outcome $Y$, and $$ \ell(a, x) = (1-\alpha) \, \|\widehat{x} - x\|_2^2 + \alpha \, (\widehat{y} - \mathbb{E}[Y \mid X=x])^2 $$ for $a =
$. Full recovery ($\alpha = 0$) as well as simple prediction ($\alpha = 1$) are special cases.
Above, we have introduced a model of feature highlighting in which an algorithm sends a subset of features to a human decision-maker. There, we have considered two different ways in which the human decision-maker may update their belief: either by taking the selection rule into account (sophisticated), or by ignoring selection (naive). We now show that these two ways of updating lead to different solutions, and that optimizing for one type of agent comes at a price when the policy is deployed for the other one.
Let $\sigma^N \in \qopname\relax n{argmin}_\sigma R^N(\sigma)$ and $\sigma^S \in \qopname\relax n{argmin}_\sigma R^S(\sigma)$ denote optimal policies for naive and sophisticated agents, respectively. To quantify the mismatch when a policy optimized for one agent type is deployed to the other, define
The next two examples show that these gaps can be arbitrarily large in either direction: a policy that is optimal for sophisticated agents may perform extremely poorly when deployed to naive agents (large $\Delta^N$), and conversely a policy optimized for naive agents can be arbitrarily suboptimal for sophisticated agents (large $\Delta^S$).
Together, (ref) and (ref) show that optimizing a highlighting policy for one belief-formation model can lead to arbitrarily poor performance when deployed to the other model. Furthermore, optimal sophisticated policies may take unintuitive forms that rely on complex relationships across the full feature vector. In (ref), we show that these findings carry over to the case where the features $X$ are continuous: even when they are Normally distributed and relatively low-dimensional, sophisticated solutions take unintuitive and hard-to-interpret forms. These findings motivate a search for simple, robust policies that remain competitive across agent types.
Above, we have shown that optimal highlighting policies can differ substantively by whether they optimize for naive or sophisticated decision-makers. We now show that this difference extends to our ability to compute optimal policies.
To show a computational contrast between sophisticated and naive receivers, we restrict our attention to discrete instance distributions. Let $n:=|\qopname\relax n{\mathbf{supp}}(\mathbb{P})|$ denote the number of possible instances in the support, $d$ the number of machine-observed features, and $k$ the bandwidth constraint.
Even with binary features and the smallest nontrivial bandwidth $k=1$, optimizing a highlighting policy for a sophisticated agent is NP-hard. The following theorem formalizes our NP-hardness result by a reduction from Euclidean $2$-means clustering.
The above result shows that determining the optimal highlighting policy for a sophisticated agent is NP-hard, even when $k=1$. In this subsection, we characterize optimal highlighting for a naive agent. The naive model exhibits a different computational complexity from the sophisticated model: in particular, the machine's optimization problem is polynomial-time solvable when $k$ is a fixed constant.
A key advantage of the naive model is computational. Because the naive agent treats the selection event as exogenous, the machine can evaluate the realized loss under any candidate revealed set $I$ pointwise for each realized instance $x$ by computing the naive posterior $\mathbb{P}(\cdot\mid X_I=x_I)$ and the induced Bayes action. When the bandwidth $k$ is bounded, this yields an exact algorithm via enumeration; we also present three scalable heuristics that will be useful in binary and correlated settings.
\paragraph{Exact optimization by enumeration.} For each realized instance $x$, define the realized loss induced by revealing $(I,x_I)$ under the naive posterior: $$ L^N(I;x)\;:=\;\ell\!\left(\widehat a\!\left(\ell,\mathbb{P}(\cdot\mid X_I=x_I)\right),\,x\right). $$ The naive--optimal policy at $x$ is obtained by minimizing $L^N(I;x)$ over all $|I|\le k$. The exact optimization algorithm would enumerate all possible $I$ and calculate the loss ((ref)). The following remark implies that if $k$ is small, then this algorithm can find the optimal policy in polynomial time.
When posterior updates are expensive, the model is high-dimensional, or the bandwidth is relatively large, then complete enumeration may still be computationally unattractive.
\paragraph{A fast first-moment heuristic.} An alternative for real-valued features $X_i$ is to highlight features whose realized values deviate most from their marginal means. Let $\mu_i:=\mathbb{E}[X_i]$ and define $s_i(x):=|x_i-\mu_i|$. The deviation heuristic selects the $k$ coordinates with the largest scores ((ref)). Indeed, the algorithm can be seen as using a surprise-based heuristic: it reports those components that represent the largest surprise relative to their expectation. If two scores are equal, we break ties by choosing the one with the smallest index, which provides additional information for the sophisticated agent. This rule ignores correlations and higher-order structure; nevertheless, in the independent Bernoulli recovery benchmark of (ref), it is optimal.
\paragraph{Marginal heuristic.} Another fast contextual rule evaluates each feature only once, starting from the empty highlighted set. For each coordinate $j\in[d]$, define the singleton marginal improvement $$ \Delta(j\mid \emptyset,x)\;:=\;L^N(\emptyset;x)-L^N(\{j\};x). $$ The marginal heuristic computes these one-step gains, ranks features by $\Delta(j\mid \emptyset,x)$, and highlights the top $k$ coordinates ((ref)). Unlike the deviation heuristic, this rule can account for correlations through the posterior induced by revealing a single feature. Unlike the greedy rule below, however, it does not update the ranking after earlier features have been selected, and therefore ignores overlap across the chosen set.
\paragraph{Greedy information gain.}
Another scalable design is a greedy policy that builds the highlighted set sequentially by maximizing the one-step reduction in the realized loss at the realized instance $x$, where the action is chosen as a Bayes action under the naive posterior. For a candidate coordinate $j\notin I$, define the marginal improvement $$ \Delta(j\mid I,x)\;:=\;L^N(I;x)-L^N(I\cup\{j\};x). $$ Starting from $I=\emptyset$, the algorithm repeatedly adds the coordinate with the largest $\Delta(j\mid I,x)$, as long as this improvement is positive ((ref)).
\paragraph{Relationship among the algorithms.} (ref) is exact and polynomial-time for constant $k$. (ref) is a fast heuristic that uses only first moments. (ref) is an intermediate rule as it accounts for the posterior effect of revealing each feature individually, but it ignores redundancy across selected features because it never updates the ranking after a coordinate is added. (ref) is a greedy algorithm that accounts for belief updates and can exploit correlations: revealing one feature can change the posterior over others. In the independent Bernoulli recovery benchmark ((ref)), (ref) and (ref) reduce to (ref) and are optimal, so they lead to the same highlight sets as (ref).
Above, we have considered general solutions for optimally highlighting features that apply for general features and loss functions. There we have shown that optimal solutions as well as the computational complexity of finding them depend on how beliefs are formed. In this section, we consider the specific case of binary features (i.e., $\mathcal{X}=\{0,1\}^d$) with the loss function given by the recovery loss $\ell(a,x) = \|a - x \|_2^2$. Our goal is to characterize the asymptotic performance of the computationally attractive, simple greedy-type algorithms from the previous section.
In order to illustrate optimal solutions explicitly and characterize their performance, we first consider naive--optimal highlighting when features are independent. We compare contextual highlighting to fixed subset selection, highlighting a fundamental difference between ex-ante and ex-post selection. We argue that greedy-style algorithms can perform well and serve as candidate “universal” policies that remain competitive for sophisticated agents while being robust for naive agents. Finally, we discuss extensions to weakly correlated settings.
We first solve for optimal highlighting policies for naive updaters in the case when features are independent Bernoulli (but not necessarily identically distributed). Specifically, let $X_1,\dots,X_d$ be independent with $X_i\sim\mathrm{Bern}(p_i)$ and $p_i=\mathbb{E}[X_i]$. Consider the squared recovery objective with $A=\mathbb{R}^d$ and $ \ell(a,X)=\|a-X\|_2^2=\sum_{i=1}^d (a_i-X_i)^2. $ If the machine reveals $(I,X_I)$, then under the naive posterior the Bayes action is $$ \widehat a_i=
$$ and therefore the realized loss at instance $X$ equals
\paragraph{Fixed subset benchmark (ex-ante selection).} A fixed subset policy chooses a single set $I^\star$ with $|I^\star|\le k$ and reveals it for every instance. Taking expectation in (ref) gives $$ \mathbb{E}[L^N(I;X)] =\sum_{i\notin I} \mathbb{E}[(X_i-p_i)^2] =\sum_{i\notin I} \operatorname{Var}(X_i) =\sum_{i\notin I} p_i(1-p_i). $$ Hence, the optimal fixed subset reveals the $k$ coordinates with the largest variances $p_i(1-p_i)$.
\paragraph{Contextual highlighting (ex-post selection).} A contextual policy may choose $I$ as a function of the realized instance $X$. Because the naive realized loss (ref) is additive across coordinates and depends on each coordinate only through $(X_i-p_i)^2$, the per-instance optimal rule is immediate.
\paragraph{Contextual can beat fixed subset.} Since a fixed subset policy is a special case of a contextual policy, it follows immediately that contextual highlighting weakly dominates fixed subset selection: $$ R^N(\sigma^N) = \mathbb{E}\!\left[\qopname\relax n{min}_{I:\,|I|\le k}\ \sum_{i\notin I} (X_i-p_i)^2\right] \ \le\ \qopname\relax n{min}_{I:\,|I|\le k}\ \mathbb{E}\!\left[\sum_{i\notin I} (X_i-p_i)^2\right] =R^N(\sigma^{\mathrm{fix}}) . $$ Moreover, the inequality is strict whenever the identity of the $k$ largest surprise terms is not almost surely constant. Intuitively, fixed subset selection hedges against uncertainty in expectation, whereas contextual selection exploits instance-level variation by revealing whichever coordinates happen to be most informative for that particular $x$.
\paragraph{Algorithmic implication.} In the independence setting, by (ref), (ref) (deviation) is optimal. Furthermore, (ref) (marginal heuristic) and (ref) (greedy information gain) coincide with (ref): revealing coordinate $i$ eliminates the term $(x_i-p_i)^2$ from (ref), so the best marginal improvement is attained by the largest current surprise.
We now solve for the asymptotic risk of the above policy for a naive and for a sophisticated updater. In order to calculate approximate losses under the above policies, we consider sequences of distributions \(\mathbb{P}_d\) over \(X_d = (X_{d,1},\ldots,X_{d,d})\) with independent coordinates for each \(d\). Each such distribution \(\mathbb{P}_d\) is given by the marginal probabilities
We are specifically interested in the case where highlighting matters in a limit. Therefore, we assume that the bandwidth \(k\) itself increases with the dimension:
In order to derive closed-form expressions for the expected loss under the above policies, we assume that the sequence $(p_d)_{d \geq 1}$ is stable in the sense that the distribution over the $p_{d,i}$ themselves converges to a distribution over the unit interval with CDF $F$:
This assumption leaves the $p_{d,i}$ flexible, and merely assumes that their distribution across $i$ can be approximated well by some function $F$.
For formulating our results, it will be convenient to transform the distributions $p_d$ and realizations $X_d$. Specifically, for all $d, i, t$, let
Then $(p_{d,i}^*)_{d,i}, F^*$ fulfills (ref) with $F^*$ continuously and (weakly) monotonically increasing. Furthermore, by the symmetry of the loss function, we can focus on highlighting the transformed features $X^*_d$.
We now formulate our main policies of interest in terms of the transformed quantities $p^*_d, X^*_d$. For every $d$ consider a (fixed) ordering $(p^*_{d,(1)},\ldots, p^*_{d,(d)})$ of $p^*$ such that the $p^*_{d,(j)}$ are monotonically increasing, with corresponding realizations $X^*_{d,(j)} \sim \text{Bern}(p^*_{d,(j)})$. Then the two highlighting choices of interest can, without loss of generality, be written as:
For developing our results, it will be helpful to consider a third highlighting scheme:
To establish the following results, we show that (ref) and (ref) are asymptotically equivalent for the right value of $\beta$, which also allows us to characterize their asymptotic gap to (ref). In order to state these results, it will be helpful to consider the quantile function
corresponding to the cdf $F^*$, which is its generalized inverse. Based on $Q^*$, we first characterize the asymptotic risk for fixed highlighting, where the highlighted set is chosen ex-ante.
We next provide an explicit expression for highlighting surprises based on a fixed fraction of features.
Assuming that the asymptotic bandwidth is not too large, we can find a fraction $\beta$ such that Procedures (ref) and (ref) coincide.
Putting these results together, we obtain an exact characterization of the limiting risks along our asymptotic sequence.
(ref) illustrates the qualitative difference between ex-ante fixed subset selection and contextual (data-driven) highlighting. We consider a sequence of independent Bernoulli features $X_{d,i}\sim\mathrm{Bern}(p_{d,i})$ whose empirical distribution of means converges to the symmetric triangular density $f(p)=4p$ for $p\in[0,\tfrac12]$ and $f(p)=4-4p$ for $p\in[\tfrac12,1]$. Fix $\alpha=\tfrac14$ so that $k= d / 4$.
Under an optimal ex-ante fixed policy ((ref)), the designer chooses one subset of size $k$ before observing $X_d$; for squared-error recovery, this amounts to prioritizing features with the largest intrinsic uncertainty $p_i(1-p_i)$, i.e., those with $p_i$ closest to $\tfrac12$ (blue region). In contrast, the optimal contextual policy ((ref)) conditions on the realized instance and highlights the coordinates with the largest realized deviation $|X_i-p_i|$. As $d\to\infty$, this “surprise-driven” rule concentrates highlighting on extreme means, producing the triangular regions shown in orange.
A simpler numerical example is given by the case where all probabilities are the same, $p_{d,i}=p$ for all $d$ and $i$, so that the features are i.i.d. We assume without loss of generality that $p \leq \frac{1}{2}$. Then $Q^*(q)=p$ for all $q\in(0,1)$. By (ref), the asymptotic normalized risk of the fixed highlighting scheme equals \[ \lim_{d\to\infty} R^N(\sigma^{\ref{enum:fixed}}) = \lim_{d\to\infty} R^S(\sigma^{\ref{enum:fixed}}) = \int_{0}^{1-\alpha} Q^*(q)\bigl(1-Q^*(q)\bigr)\,\textnormal{d} q = (1-\alpha)\,p(1-p). \] By (ref), $\beta^*$ solves $\int_{0}^{\beta^*} Q^*(q)\,\textnormal{d} q = \beta^* p = \alpha$, so $\beta^*=\alpha/p$ (and we assume that $\alpha < p$ by (ref)). The greedy risk has normalized asymptotic risk \[ \lim_{d\to\infty} R^S(\sigma^{\ref{enum:greedy}}) = \int_{\beta^*}^{1} Q^*(q)\bigl(1-Q^*(q)\bigr)\,\textnormal{d} q = (1-\beta^*)\,p(1-p) = (p-\alpha)(1-p) \] for the sophisticated agent, and asymptotic normalized risk
for the naive agent. As $\alpha \rightarrow p$, the sophisticated agent achieves an average risk approaching zero, the naive agent achieves an average risk $p^2 (1-p)$, and a fixed highlighting scheme achieves an average risk $p (1-p)^2$.
In the previous subsection, we focused on independent features, where it is optimal for a naive receiver to order features by their marginal information value and reveal as many features as the bandwidth constraint allows. With correlation, however, the value of highlighting also depends on its implication for unrevealed features. For a naive receiver who ignores the selection rule, revealing an additional feature can even increase the realized loss in some instances. The next example shows that, in correlated settings, a naive optimal contextual policy need not be monotone in the amount of information highlighted. In particular, it may be optimal to withhold information in some cases.
(ref) also illustrates why the deviation heuristic ((ref)) and the marginal heuristic ((ref)) can be suboptimal under correlation, whereas greedy information gain ((ref)) can adapt by withholding information when the best available reveal would increase the realized loss. In (ref) with $k=1$, the marginal means are $\mu_1=\mu_2=\mathbb{E}[X_i]=1/3$. (ref) reveals one coordinate at $X=(0,0)$, and incurs loss $1/4$ there, while achieving zero loss at $X=(0,1)$ and $X=(1,0)$. Hence $$ R^N(\sigma^{\mathrm{dev}})=\frac13\cdot\frac14=\frac{1}{12}. $$ By contrast, greedy information gain with early stopping selects $I=\emptyset$ at $X=(0,0)$ (loss $2/9<1/4$) and reveals the “$1$” coordinate in the other two states, achieving zero loss there. Therefore $$ R^N(\sigma^{\mathrm{greedy}})=\frac13\cdot\frac{2}{9}=\frac{2}{27} \;<\; \frac{1}{12}. $$
The above examples show cases where $\sigma^{\mathrm{greedy}}$ is a better selection rule than other approximate algorithms. However, the following remark indicates that sometimes (ref) can perform worse than (ref) and (ref).
The previous remark relies on (ref)'s early-stopping rule. Even without early stopping, (ref)'s myopic first-step choice can lock it out of the optimal pair, as the following discrete example shows.
\paragraph{Good approximation for the correlation case under a weak-mean-shift assumption.}
A simple sufficient assumption is that conditioning on a small number of revealed coordinates does not substantially change posterior means of unrevealed coordinates.
(ref) says that even after observing up to $k$ coordinates, each remaining coordinate's conditional mean stays within $\varepsilon$ of its unconditional mean. This holds, for example, under standard weak-dependence or bounded-influence regimes.
The simple deviation heuristic is close to optimal under the above assumption, provided that the bound $\varepsilon$ is sufficiently small.
We now illustrate our theoretical results in a calibrated numerical exercise using data from the American Housing Survey (AHS). Home valuation is a canonical decision with many potentially relevant attributes: a prospective buyer or appraiser cares about structural characteristics, neighborhood quality, and price, yet typically lacks the bandwidth to inspect every detail of every listing. In such settings, an algorithm can support the decision-maker by highlighting a small subset of attributes that are most informative for getting a realistic impression and assessing the value of each home.
For our specific application, we leverage data from 1,521 homes in the Minneapolis--St. Paul--Bloomington metro area, model the human's prior as a multivariate Gaussian over 44 housing characteristics, and compare a range of highlighting policies primarily from the perspective of a naive agent, with a supplementary robustness exercise for a stylized sophisticated agent. The exercise yields three main takeaways that mirror the theory: (1) contextual highlighting delivers substantial gains over fixed, ex-ante highlighting; (2) taking covariance into account is important, since there is otherwise substantive redundancy across selected features; and (3) it can sometimes be optimal to highlight less rather than more, as revealing additional features can increase the loss faced by a naive agent in correlated environments.
We use the pooled 2021 and 2023 AHS metropolitan samples, restricting to owner-occupied units with an observed self-reported market value (MARKETVAL) in the Minneapolis--St. Paul--Bloomington metro area ($n=1{,}521$). The state vector has 44 features, including $\log(\texttt{MARKETVAL})$, structural characteristics (unit size, stories, lot size, number of bedrooms, bathrooms, and total rooms), building type, ownership status, heating and cooling systems, condition indicators, and neighborhood quality ratings. For simplicity, we treat all features as real values.
We model the state as a multivariate Gaussian over the 44 features, with the prior mean and covariance estimated from the data. The price coordinate is stored as $\log(\texttt{MARKETVAL})$; its prior mean is 12.6725, corresponding to approximately \$319{,}000 in the original dollar scale. When a set $S$ of features is revealed, the naive agent updates to the Gaussian posterior conditional on $X_S$, leaving unrevealed coordinates at their conditional expectations.
We use a loss function that is equivalent to the outcome-targeted recovery loss from (ref). Specifically, for $Y = \log(\texttt{MARKETVAL})$, we use the loss function
where $w_j$ are feature-specific importance weights and $\sigma_j^2$ is the sample variance of each variable. The weight on $\log(\texttt{MARKETVAL})$ is fixed exogenously at $\alpha=\tfrac{1}{2}$; the remaining weights are derived from the coefficients of a ridge regression of $\log(\texttt{MARKETVAL})$ on the other features ($R^2=0.51$). We then evaluate choices by the average sample loss
By construction, the no-reveal benchmark achieves a loss of exactly one. All results below refer to the main specification in which MARKETVAL is not directly revealable.
We compare several policies, organized along two margins emphasized in the theory: fixed versus contextual highlighting, and covariance-aware versus covariance-ignorant selection.
For small bandwidths we also compute exact enumeration benchmarks. On the fixed side, we enumerate all subsets for $k \leq 3$ to obtain the optimal ex-ante subset under the current objective. On the contextual side, we also run exact enumeration ((ref)) for $k \leq 3$ on the full one-metro sample. This is computationally feasible in the current application and puts the exact contextual benchmark on the same footing as the other policies.
(ref) reports the main results, combining all fixed and contextual policies in a single table to facilitate comparison across the two margins.
\paragraph{Fixed versus contextual.} Contextual policies uniformly outperform their fixed-policy counterparts at every budget we consider, and the gap is quantitatively large. At $k=1$, for example, fixed forward stepwise attains a loss of 0.7616, while contextual greedy attains 0.3917. The gap widens as the budget increases: at $k=10$, contextual greedy attains 0.1603 against 0.3851 for fixed forward stepwise. The advantage of contextual over fixed highlighting is therefore first-order in this realistic data environment.
\paragraph{The role of correlation in fixed policies.} Among fixed policies, the comparison between marginal value and forward stepwise isolates the cost of ignoring correlation. Both policies use the full covariance structure to evaluate each feature's informativeness, but marginal value evaluates features one at a time while forward stepwise conditions on the features already selected. At $k=1$ the two coincide, both selecting UNITSIZE, the most informative single feature. From $k=2$ onward, however, marginal value stacks highly correlated size and room-count variables (UNITSIZE, BATHROOMS, TOTROOMS, BEDROOMS, UNITFLOORS), while forward stepwise diversifies quickly across distinct informational dimensions (\texttt{UNITSIZE}, \texttt{BLD}, \texttt{OWNLOT}). This pattern demonstrates that accounting for covariance in the evaluation of each individual feature is not sufficient for good fixed-policy performance; one must also account for redundancy among the features jointly selected.
\paragraph{Covariance awareness on both margins.} Among fixed policies, forward stepwise uniformly improves on the covariance-ignorant top-$k$ ranking. The top-$k$ rule begins with highly weighted variables such as building type, bathrooms, and unit size, whereas the covariance-aware ordering diversifies more quickly. Similarly, among contextual policies, the simple deviation heuristic performs worst because it uses only first moments: its loss is 0.9291 at $k=1$ and 0.6317 at $k=3$, far above even contextual marginal top-$k$. The covariance-ignorant but posterior-aware marginal top-$k$ improves substantially on deviation, and contextual greedy performs best among the scalable contextual rules.
\paragraph{Non-monotonicity and the full-reveal benchmark.} The bottom row of (ref) reports the loss when all 43 non-price features are revealed. This full-reveal benchmark attains a loss of 0.2363, which is the irreducible error from the MARKETVAL component that cannot be perfectly predicted from the other features. Notably, contextual greedy at $k=10$ already achieves 0.1603, substantially below full reveal. Smart greedy with a budget of $k=43$ achieves 0.1322 by stopping at a median of 25 features per house, while contextual greedy without early stopping at $k=43$ matches the full-reveal loss of 0.2363. The explanation is that revealing low-weight, weakly correlated features can degrade the Gaussian posterior estimate of MARKETVAL by injecting noise through the covariance update. Early stopping avoids this by withholding features whose marginal effect on the posterior is harmful. This is the empirical counterpart of the non-monotonicity result in (ref): even in a high-dimensional, realistic setting, revealing more information need not improve outcomes.
\paragraph{Exact small-$k$ benchmarks.} The exact enumeration results confirm that the scalable heuristics are directionally accurate. On the fixed side, exact ex-ante enumeration coincides with fixed forward stepwise for $k \leq 3$, selecting \{UNITSIZE\} at $k=1$, \{BLD, UNITSIZE\} at $k=2$, and \{BLD, UNITSIZE, OWNLOT\} at $k=3$. On the contextual side, the exact oracle equals greedy at $k=1$ and improves on contextual greedy at $k=2$ and $k=3$: exact contextual loss is 0.2793 versus 0.2920 for contextual greedy at $k=2$, and 0.2278 versus 0.2494 at $k=3$. This suggests that the sequential greedy rule captures much of the value of contextual adaptation while remaining computationally tractable.
\paragraph{Sophisticated-agent performance and robustness.} We also report a stylized robustness exercise for sophisticated updating at $k\leq 3$. The naive benchmark remains the analytical Gaussian posterior throughout. For fixed policies, sophisticated and naive losses coincide because the selected set is constant ex ante. For contextual policies, we simulate sophisticated belief updates based on a simulation from the prior. Specifically, we take 100{,}000 draws from the fitted Gaussian prior, with each revealable synthetic non-price coordinate snapped to the nearest observed AHS support code before policy evaluation and conditioning. Within this sample, we group support draws by the realized selected set and the displayed revealed covariates, and take the empirical conditional mean within that support sample. This procedure presents a way of calculating posteriors based on feature values and feature selection.
(ref) reports the performance of the resulting choices on the actual AHS sample, while (ref) and (ref) report two synthetic validations. Under the correct model and exact conditioning, a sophisticated agent should weakly outperform a naive agent. The synthetic benchmarks line up with that logic, while the real-data benchmark remains slightly worse, which we interpret as evidence that the empirical selection-aware posterior is sensitive to misspecification when the true housing distribution deviates from the fitted Gaussian approximation. Furthermore, overfitting may deteriorate the performance of the more complex updating rule.
These tables support a narrow but useful conclusion. Once the sophisticated benchmark is put on the same discrete signal alphabet as the AHS data, the synthetic exercises line up with the theory: sophisticated updating improves on naive updating for the contextual policies, with the strongest gains when support and evaluation are drawn from the same discretized Gaussian environment. The deviation heuristic benefits from sophisticated updating as well in the same-sample synthetic benchmark, but its gains are much smaller than those of the posterior-based contextual rules and they disappear out of sample at $k=3$. On the real AHS sample, the empirical sophisticated proxy remains slightly worse than the Gaussian naive benchmark for all contextual policies, including deviation. We read that gap as evidence of misspecification of the Gaussian state model rather than as a substantive challenge to the theoretical dominance logic. However, it points to the practical challenge that results are heavily driven by the exact way beliefs are updated.
We discuss several extensions of our framework. First, we comment on continuous instance spaces, where the set of possible states is infinite. Second, we discuss alternative behavioral updating rules that interpolate between naive and sophisticated belief formation. Third, we incorporate private human information, which affects belief formation. Finally, we mention wrong belief and misaligned preferences as important extensions for future research.
Our main results focus on discrete distributions, where a highlighting policy maps each state in a finite support to a subset of coordinates. In many applications, however, $X$ is continuous, and the posteriors induced by a policy can be even more complex. In such settings, the designer's problem for a sophisticated receiver becomes a continuous-state information design problem. A simple illustration is a Gaussian recovery problem. Let $X=(X_1,X_2)\sim \mathcal N(0,I_2)$ and suppose the target is $y(X)=X\in\mathbb{R}^2$ with squared loss. Let $k=1$ and restrict attention to policies that reveal exactly one coordinate value. For a naive agent, revealing coordinate $j$ sets $\widehat X_j=X_j$ and leaves the other coordinate at its prior mean $0$. The optimal naive policy is therefore to reveal the coordinate with larger magnitude, i.e., $\sigma^N(x_1,x_2)\in \qopname\relax n{argmax}_{j\in\{1,2\}}|x_j|$, yielding the expected loss \[ R^N(\sigma^N) =\mathbb{E}\!\left[\qopname\relax n{min}\{X_1^2,X_2^2\}\right] \approx 0.36. \] For a sophisticated agent, however, the choice of which coordinate is revealed can itself convey information about the other coordinate. Any such policy can be represented by two prediction functions $h,g:\mathbb{R}\to\mathbb{R}$: if the policy reveals $X_1$, the receiver sets $(\widehat X_1,\widehat X_2)=(X_1,h(X_1))$; if it reveals $X_2$, it sets $(\widehat X_1,\widehat X_2)=(g(X_2),X_2)$. Thus the designer's objective can be transformed to finding $(h,g)$ to minimize \[ J(h,g)\;=\;\mathbb{E}\!\left[\qopname\relax n{min}\Big\{(X_2-h(X_1))^2,\ (X_1-g(X_2))^2\Big\}\right], \qquad (X_1,X_2)\sim\mathcal N(0,I_2). \] The induced highlighting rule is \[ \sigma(x_1,x_2)\;=\;
\] Even in this two-dimensional case, optimizing over $(h,g)$ is nontrivial. (ref) contrasts the naive partition induced by $\sigma^N$ with a more intricate partition induced by a numerically optimized pair $(h,g)$ (computed via a Lloyd-style best-response iteration), which attains expected loss \[ R^S(\sigma^{\text{complex}})\approx 0.28 < 0.36 = R^S(\sigma^N)\, \] a reduction of about $22\%$ relative to $\sigma^N$. This example illustrates that in continuous settings, sophisticated receivers turn the highlighting problem into a continuous information-design problem, and optimal policies may exhibit complex state-dependent regions even with just two dimensions and a highly symmetrical prior.
Our main model considers two benchmark belief-formation rules: sophisticated updating, which conditions on the selection event, and naive updating, which ignores it. In practice, both assumptions are natural, yet extreme benchmarks. Real decision-maker updating may also be influenced by anchoring, availability, and representativeness. As a specific behavioral deviation, we consider stereotypical updating bordalo2016stereotypes, where the agent replaces Bayesian conditioning by finding a representative instance. One stylized version is the following: after observing $(I,X_I)$, the agent selects a single “representative” \[ \widehat X \in \qopname\relax n{argmax}_{x\in\qopname\relax n{\mathbf{supp}}(\mathbb{P}):\ \ x_I= X_I}\ \mathbb{P}(X = x \mid \ X_I), \] and then plays the action that is optimal for $\widehat X$. Under squared recovery loss, this corresponds to imputing all missing coordinates by the most likely completion rather than the posterior mean. A detailed study of optimal highlighting against such behavioral rules is an interesting direction for future work.
Above, we have assumed that a decision instance is fully characterized by the vector $x$ that is available to the algorithm. In practice, the human decision-maker may have additional private information. We now allow the human to observe such private information $X_H$ in addition to the algorithm's message $(I,X_I)$. The posterior definitions in (ref) extend directly:
The design objective remains to minimize expected loss, except that the Bayes action is now computed under posteriors conditional on $X_H$.
Private information also provides an additional motivation for robust design. If the algorithm is uncertain about what $X_H$ the human has access to, a natural robust objective is to choose a policy that performs well uniformly over possible private information structures. Because additional private information can only reduce a Bayesian receiver's expected squared error, the worst case for the designer is the case in which the human observes nothing beyond the highlighted features. Consequently, finding the policy that minimizes expected loss under the assumption that $X_H=\emptyset$ may itself be viewed as a robust solution to the problem with private information.
Formally, fix a jointly distributed model for $(X_M,X_H)$ with $X_M\in\mathbb{R}^d$ the machine features available to the designer and $X_H$ an additional square-integrable signal that the human may or may not observe. Write $\mathcal H$ for the collection of such private information structures; the degenerate element $\emptyset\in\mathcal H$ corresponds to a human with no private information. For a highlighting policy $\sigma$ with $|\sigma(x)|\le k$ and a receiver type $\tau\in\{S,N\}$, let $\widehat X_M^\tau(\sigma;X_I,X_H)$ denote the induced Bayes action for reconstructing $X_M$ (note that $X_H$ is always perfectly available, so does not add loss), and define the risk with private information $H$ by \[ R^\tau(\sigma;H)\ :=\ \mathbb{E}\!\left[\bigl\|X_M-\widehat X_M^\tau(\sigma;X_I,X_H)\bigr\|_2^2\right],\qquad I=\sigma(X_M), \] with $R^\tau(\sigma;\emptyset)$ the risk defined in (ref). Throughout what follows, the revealed vector $X_I$ is understood to implicitly carry its index tag $I$, so that $\Sigma(X_I)=\Sigma(I,X_I)$ is a well-defined sub-$\sigma$-algebra of the underlying probability space.
The above minimax proposition implies that optimizing the highlighting policy for a sophisticated human with no private information delivers a robust solution against arbitrary private information channels the designer may not observe or control. However, the result does not carry over to the naive agent. For the sophisticated agent, the posterior mean is the orthogonal projection of $X_M$ onto the full information $\sigma$-field generated by the private signal and the highlighting rule, so adding information can only reduce squared loss. The naive agent ignores the informational content of the selection event, so its action is generally not the conditional expectation with respect to that richer $\sigma$-field. As a result, the projection argument behind (ref) breaks down for naive updating.
The above model assumes that both sophisticated and naive agents have a prior of the world that coincides with the actual distribution. Furthermore, principal (designer) and agent (decision-maker) choices are fully aligned. An important natural extension is to a model where both priors and preferences can differ between principal and agent. Specifically, the agent may start with a prior $\widetilde{\mathbb{P}}$ and minimize expected loss for a loss function $\widetilde{\ell}$. The principal may then still optimize for a highlighting policy for their prior $\mathbb{P}$ and loss function $\ell$, taking both frictions into account and connecting the model further to Bayesian persuasion kamenica2011bayesian. Highlighting may be an attractive way of collaboration in this case since merely revealing rather than manipulating features may still lead to reasonable solutions even in a world where principal and agent have partially misaligned preferences or different beliefs and may not fully trust each other.
We consider a model of highlighting in human--AI collaboration where an algorithm reveals a subset of features to enable a decision-maker to make better decisions about a given problem instance. Our main takeaway is that the way in which the decision-maker interprets the provided information matters for how to design good algorithms. When the decision-maker interprets the values of the revealed features in isolation, simple algorithms perform close to optimally. However, when the decision-maker also interprets why information was revealed, optimal algorithms are more complex and may confuse naive decision-makers. Beyond these specific assumptions about how information is interpreted, our approach points to an important agenda of modeling how decision-makers interpret information and deriving tractable highlighting algorithms as a practical tool to achieve human--AI complementarity.