# Evaluating AI Investment Strategies

arXiv: https://arxiv.org/abs/2606.08791 · HTML: https://mlsanity.com/paper/2606.08791/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 55 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Builds on (most cited first, 4 of 4)

- [Minimax Regret Bounds for Reinforcement Learning](https://mlsanity.com/paper/1703.05449/) (2017)
- [Preventing Fairness Gerrymandering: Auditing and Learning for Subgroup Fairness](https://mlsanity.com/paper/1711.05144/) (2017)
- [Smart "Predict, then Optimize"](https://mlsanity.com/paper/1710.08005/) (2017)
- [Regret Equals Covariance: A Closed-Form Characterization for Stochastic Optimization](https://mlsanity.com/paper/2605.14019/) (2026)

## Abstract (arXiv)

We study the problem of auditing a black-box algorithmic decision-maker from observable inputs and outputs alone. Our main result is an exact decomposition: under precisely characterized conditions, the cumulative regret of a dynamic policy equals the sum of per-period covariances between the cost vector and the policy's decision. This extends the single-period identity of Aldridge~(2026) to the full multi-period setting of stochastic dynamic programming. We prove the identity holds exactly under i.i.d. costs and mean-unbiased Markov policies, derive closed-form bias corrections for non-stationary and time-varying cases, and establish the discounted-horizon analog. A Bellman recursion for the covariance regret functional connects the result to standard reinforcement learning algorithms; for rolling-window policies, the estimation-error bias is O(d/w). The decomposition has direct implications for algorithmic auditing in strategic environments: in platform mechanism design, it provides a welfare-based audit metric without access to the agent's private type; in repeated games, covariance reduction is a sufficient condition for policy improvement; in procurement and ad auctions, the bias correction quantifies welfare loss from strategic misreporting. The associated trajectory estimator is consistent, asymptotically normal with HAC variance, and computable in O(T · nd) time. This makes the proposed approach a tractable, model-free audit tool for platform mechanisms, algorithmic portfolio strategies, and any sequential decision system subject to external performance review.