Planning in entropy-regularized Markov decision processes and games

The headline result is the polynomial bound itself, but the more important detail is the two-player extension: most prior work on regularized MDPs stops at single-agent settings, and extending worst-case guarantees to adversarial games is a meaningfully harder problem that the summary underplays.

This connects most directly to the log-barrier regularization paper covered on April 16, which proved optimal last-iterate convergence in zero-sum matrix games using a different regularization approach. Both papers are working on the same underlying problem, namely how regularization can restore tractability in game-theoretic planning, but from different angles: that paper focused on bandit feedback and convergence rates, while SmoothCruiser targets sample complexity in the full MDP setting. The LLM shortest-path generalization piece from April 16 is also loosely relevant, since it identified horizon length as a hard wall for learned planners, and formal planning algorithms with polynomial guarantees represent the classical alternative to that learned approach.

Watch whether SmoothCruiser's O(1/epsilon^4) bound holds in empirical benchmarks against the log-barrier method from the April 16 paper. If practitioners find the constant factors prohibitive at realistic epsilon values, the theoretical gap over non-regularized methods may not translate to usable performance.