New Mathematical Framework for Auditing Black-Box AI Decision Systems
Researchers have developed an exact decomposition theorem that allows external auditors to evaluate the performance and welfare implications of black-box algorithmic decision-makers using only observable inputs and outputs. The work extends a single-period identity from prior research to the full multi-period setting of stochastic dynamic programming, connecting cumulative regret to per-period covariances between cost vectors and policy decisions. The framework has broad applications in auditing AI systems used in platform mechanisms, ad auctions, procurement, and algorithmic portfolio management without requiring access to proprietary model internals.
A new preprint posted to arXiv presents a covariance-based decomposition that equates the cumulative regret of a dynamic policy to the sum of per-period covariances between a cost vector and the policy's decisions, under conditions of i.i.d. costs and mean-unbiased Markov policies. The result generalizes a single-period identity attributed to Aldridge (2026) into the multi-period stochastic dynamic programming setting, with closed-form bias corrections derived for non-stationary and time-varying environments, as well as a discounted-horizon analog. A Bellman recursion links the covariance regret functional to standard reinforcement learning algorithms, and for rolling-window policies the estimation-error bias is shown to be O(d/w). The associated trajectory estimator is proven to be consistent, asymptotically normal with HAC variance, and computable in O(T·nd) time, making it practically tractable. Applications highlighted include welfare-based auditing of platform mechanisms without access to agents' private types, a covariance-reduction condition for policy improvement in repeated games, and quantification of welfare loss from strategic misreporting in procurement and ad auctions.
What's missing
The paper has not yet undergone peer review, as it is a preprint. Empirical validation on real-world platform or auction data is not described in the abstract; it is unclear whether the theoretical guarantees hold robustly under practical violations of the i.i.d. and mean-unbiased Markov policy assumptions. The relationship to and advantages over existing black-box auditing methods in the literature are not detailed in the abstract.
What different sources said
- arXiv cs.AICenter
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