Irene Aldridge
arXiv 21 Jul 2026 · Econometrics
arXiv:2607.18866 · PDF · Extracted main text
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.
appendix boundary found by none_found · 100% of the source is main text. Read the extracted text to check this.
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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| aldridge2026 | unmatched citation key aldridge2026 | 0.843 | 3 | 3 | 100% |
| 2 | Agrawal, Shipra and Goyal, Navin (2013) Further Optimal Regret Bounds for Thompson Sampling | 0.644 | 2 | 2 | 100% |
| 3 | Chen, Hao and Didisheim, Antoine and Somoza, Luis A (2026) Out of the Black Box: Uncertainty Quantification for LLMs via Conditional Probabilities | 0.405 | 1 | 1 | 100% |
| 4 | Hart, Sergiu and Mas-Colell, Andreu (2000) A Simple Adaptive Procedure Leading to Correlated Equilibrium | 0.405 | 1 | 1 | 100% |
| 5 | Hazan, Elad and Agarwal, Amit and Kale, Satyen (2007) Logarithmic Regret Algorithms for Online Convex Optimization | 0.405 | 1 | 1 | 100% |
| 6 | Helmbold, David P. and Schapire, Robert E. and Singer, Yoram and War… (1998) On-Line Portfolio Selection Using Multiplicative Updates | 0.405 | 1 | 1 | 100% |
| 7 | Shalev-Shwartz, Shai (2007) Online Learning: Theory, Algorithms, and Applications | 0.405 | 1 | 1 | 100% |
| 8 | Zinkevich, Martin and Bowling, Michael and Johanson, Michael and Pic… (2007) Regret Minimization in Games with Incomplete Information | 0.405 | 1 | 1 | 100% |
| cover1991 | unmatched citation key cover1991 | 0.405 | 1 | 1 | 100% |
| hazan2016 | unmatched citation key hazan2016 | 0.405 | 1 | 1 | 100% |
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.