Evaluating AI Investment Strategies

• URL: http://arxiv.org/abs/2606.08791v1
• Date: Sun, 07 Jun 2026 19:16:50 GMT
• Title: Evaluating AI Investment Strategies
• Abstract summary: We study the problem of auditing a black-box algorithmic decision-maker from observable inputs and outputs alone.<n>Under precisely characterized conditions, the cumulative emphregret of a dynamic policy equals the sum of per-period covariances between the cost vector and the policy's decision.<n>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.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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 \emph{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 $O(T \cdot nd)$ 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.

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