aiqbench analysis
This research provides a tractable, model-free framework for auditing black-box decision systems by decomposing cumulative regret into observable per-period covariances. The method offers practical tools for welfare-based auditing in platform mechanisms and quantifies welfare losses in strategic environments like ad auctions without requiring access to private agent data. Its computational efficiency and theoretical rigor make it a significant advancement for algorithmic accountability in sequential decision-making systems.
Evaluating AI Investment Strategies
arXiv:2606.08791v1 Announce Type: cross 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.
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.
Econometrics (econ.EM); Artificial Intelligence (cs.AI); Portfolio Management (q-fin.PM); Risk Management (q-fin.RM); Statistical Finance (q-fin.ST)
arXiv:2606.08791 [econ.EM]
(or arXiv:2606.08791v1 [econ.EM] for this version)
https://doi.org/10.48550/arXiv.2606.08791 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 318 words
