Researchers present a mathematical framework for auditing black-box algorithmic decision-makers by decomposing cumulative regret into per-period covariances between costs and policy decisions. The model-free approach enables practical auditing of sequential decision systems, with applications to platform mechanisms, repeated games, and algorithmic trading strategies without requiring access to private agent information.
This paper addresses a fundamental challenge in algorithmic accountability: how to evaluate opaque decision-making systems using only observable inputs and outputs. The core contribution—an exact decomposition of cumulative regret into covariance terms—provides auditors with a mathematically rigorous tool for assessing policy performance without model specification or access to proprietary algorithms.
The work extends prior single-period analysis to dynamic, multi-period settings relevant to real-world sequential decision problems. The authors establish that under i.i.d. cost conditions and mean-unbiased Markov policies, regret decomposes cleanly, with extensions to non-stationary and time-varying environments. This theoretical advance connects to standard reinforcement learning frameworks through Bellman recursions, bridging academic theory with practical implementation.
For platform operators and regulators, this framework offers significant advantages. In mechanism design contexts, auditors can measure welfare losses from strategic behavior without observing agents' private information—a critical capability for evaluating fairness in marketplaces. In procurement and ad auctions, the bias corrections quantify welfare degradation from misreporting. The computational efficiency—O(T·nd) complexity—makes the approach tractable for real-time monitoring of complex systems.
The consistency and asymptotic normality properties of the trajectory estimator enable statistical inference around audit conclusions, adding rigor to platform accountability claims. Organizations deploying algorithmic trading strategies, portfolio management systems, or marketplace mechanisms can now implement formal audit procedures without disclosing proprietary decision logic. This development supports regulatory objectives around algorithmic transparency while protecting legitimate competitive interests.
- →Exact regret decomposition into covariance terms enables model-free auditing of black-box algorithms using only observable data.
- →Framework applies to platform mechanisms, repeated games, and auctions without requiring access to agents' private information or proprietary algorithms.
- →Computational efficiency of O(T·nd) makes the approach practical for real-time monitoring of complex sequential decision systems.
- →Asymptotically normal estimator with HAC variance enables statistical inference and rigor in audit conclusions.
- →Bias corrections quantify welfare losses from strategic misreporting in procurement and ad auction contexts.