Sequential Off-Policy Learning with Logarithmic Smoothing

TL;DR

This paper introduces a new algorithm for sequential off-policy learning that combines Logarithmic Smoothing with PAC-Bayesian analysis, outperforming existing methods in dynamic policy update scenarios.

Contribution

The work presents a simple, theoretically grounded algorithm for sequential off-policy learning that generalizes previous approaches and improves performance with policy updates.

Findings

The proposed algorithms match state-of-the-art offline methods in batch settings.

They outperform traditional methods in sequential policy update scenarios.

Empirical results demonstrate the benefits of the sequential framework and the proposed algorithms.

Abstract

Off-policy learning enables training policies from logged interaction data. Most prior work considers the batch setting, where a policy is learned from data generated by a single behavior policy. In real systems, however, policies are updated and redeployed repeatedly, each time training on all previously collected data while generating new interactions for future updates. This sequential off-policy learning setting is common in practice but remains largely unexplored theoretically. In this work, we present and study a simple algorithm for sequential off-policy learning, combining Logarithmic Smoothing (LS) estimation with online PAC-Bayesian tools. We further show that a principled adjustment to LS improves performance and accelerates convergence under mild conditions. The algorithms introduced generalise previous work: they match state-of-the-art offline approaches in the batch case and substantially outperform them when policies are updated sequentially. Empirical evaluations highlight both the benefits of the sequential framework and the strength of the proposed algorithms.