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Optimizing Regret

Irene Aldridge

arXiv 21 Jul 2026 · Econometrics

arXiv:2607.18866 · PDF · Extracted main text

Abstract

Building on the identity that expected regret equals the covariance between costs and decisions, this paper develops the complete derivative theory of the covariance regret functional. We derive the Gâteaux derivative, showing that the universal steepest-descent direction is the contrarian policy $-(c-\bar{c})$, while ascent yields momentum. For linear policies $\hatπ(c) = Ac+b$, the gradient is the cost covariance matrix $Σ_c$, with a zero Hessian implying boundary-optimal solutions such as the minimum-variance portfolio. We extend to constrained optimization, sign-gradient duality between regret minimization and alpha maximization, finite-sample convergence bounds paralleling Thompson Sampling, and gradient-descent algorithms requiring only input observations, with applications to portfolio tilting and LLM-based allocation strategies.

Citation extraction

7
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15
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12
distinct cited
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main-text words

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
aldridge2026unmatched citation key aldridge20260.84333100%
2Agrawal, Shipra and Goyal, Navin (2013) Further Optimal Regret Bounds for Thompson Sampling0.64422100%
3Chen, Hao and Didisheim, Antoine and Somoza, Luis A (2026) Out of the Black Box: Uncertainty Quantification for LLMs via Conditional Probabilities0.40511100%
4Hart, Sergiu and Mas-Colell, Andreu (2000) A Simple Adaptive Procedure Leading to Correlated Equilibrium0.40511100%
5Hazan, Elad and Agarwal, Amit and Kale, Satyen (2007) Logarithmic Regret Algorithms for Online Convex Optimization0.40511100%
6Helmbold, David P. and Schapire, Robert E. and Singer, Yoram and War… (1998) On-Line Portfolio Selection Using Multiplicative Updates0.40511100%
7Shalev-Shwartz, Shai (2007) Online Learning: Theory, Algorithms, and Applications0.40511100%
8Zinkevich, Martin and Bowling, Michael and Johanson, Michael and Pic… (2007) Regret Minimization in Games with Incomplete Information0.40511100%
cover1991unmatched citation key cover19910.40511100%
hazan2016unmatched citation key hazan20160.40511100%

Showing the top 10 of 12 scored citations. 3 of these could not be matched to a bibliography entry, so only the citation key is shown.