New RL Algorithm Achieves Horizon-Free Optimal Regret

Runlong Zhou, Zihan Zhang, Maryam Fazel, Simon S. Du· July 23, 2026 View original

Summary

Researchers propose a new reinforcement learning algorithm for finite-horizon time-homogeneous tabular Markov Decision Processes that achieves asymptotically optimal regret without dependence on the horizon length (H). This significantly improves upon previous guarantees by removing the log H factor and drastically improving the asymptotic bound.

In the field of reinforcement learning, minimizing regret for finite-horizon time-homogeneous tabular Markov Decision Processes (MDPs) has been a significant challenge, particularly in achieving performance independent of the horizon length (H). Previous algorithms often included a `log H` factor or had less optimal asymptotic bounds. A new algorithm has been introduced that offers an asymptotically optimal regret bound, specifically `O(sqrt(SAK) + S^8A^3)`, where S is states, A is actions, and K is episodes. This bound matches the contextual-bandit lower bound `O(sqrt(SAK))` up to logarithmic factors, effectively removing the `log H` dependence seen in prior work and substantially improving the asymptotic performance. The key technical innovations include exploiting the monotonicity of optimal value functions, projecting them onto an S-dimensional grid to avoid additional factors, and introducing a horizon-truncation argument for reward-based exploration. Additionally, a cutting bonus preserving optimism and monotonicity, and a new bound on total deviation for time-homogeneous MDPs, contribute to this breakthrough.

Why it matters

Professionals developing or deploying reinforcement learning agents in environments with varying or unknown horizons can now achieve more robust and efficient learning, leading to better decision-making systems in complex scenarios.

How to implement this in your domain

  1. 1Investigate the new algorithm for applications where horizon-free regret is critical, such as long-term planning or continuous learning systems.
  2. 2Benchmark the algorithm against existing RL methods in simulated environments to quantify performance gains.
  3. 3Collaborate with research teams to understand the practical implications and potential adaptations for specific business problems.
  4. 4Train ML engineers on advanced RL techniques, including horizon-free regret minimization.

Who benefits

RoboticsAutonomous SystemsFinanceLogisticsGaming

Key takeaways

  • A new RL algorithm achieves asymptotically optimal regret without dependence on the horizon length.
  • It significantly improves upon previous bounds by removing the `log H` factor.
  • Technical innovations include exploiting value function monotonicity and a horizon-truncation argument.
  • This breakthrough enables more efficient and robust RL in complex, time-homogeneous MDPs.

Original post by Runlong Zhou, Zihan Zhang, Maryam Fazel, Simon S. Du

"arXiv:2607.19854v1 Announce Type: new Abstract: We study horizon-free regret minimization for finite-horizon time-homogeneous tabular Markov decision processes with $S$ states, $A$ actions, horizon $H$, and per-trajectory total reward bounded by $1$. We propose a new algorithm an…"

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Originally posted by Runlong Zhou, Zihan Zhang, Maryam Fazel, Simon S. Du on X · view source

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