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Mirror Descent Policy Optimization

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arxiv 2005.09814 v5 pith:FIN5YJAD submitted 2020-05-20 cs.LG cs.AIstat.ML

Mirror Descent Policy Optimization

classification cs.LG cs.AIstat.ML
keywords mdpoalgorithmstrust-regiondescentmirrorobjectiveoptimizationpolicy
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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Mirror descent (MD), a well-known first-order method in constrained convex optimization, has recently been shown as an important tool to analyze trust-region algorithms in reinforcement learning (RL). However, there remains a considerable gap between such theoretically analyzed algorithms and the ones used in practice. Inspired by this, we propose an efficient RL algorithm, called {\em mirror descent policy optimization} (MDPO). MDPO iteratively updates the policy by {\em approximately} solving a trust-region problem, whose objective function consists of two terms: a linearization of the standard RL objective and a proximity term that restricts two consecutive policies to be close to each other. Each update performs this approximation by taking multiple gradient steps on this objective function. We derive {\em on-policy} and {\em off-policy} variants of MDPO, while emphasizing important design choices motivated by the existing theory of MD in RL. We highlight the connections between on-policy MDPO and two popular trust-region RL algorithms: TRPO and PPO, and show that explicitly enforcing the trust-region constraint is in fact {\em not} a necessity for high performance gains in TRPO. We then show how the popular soft actor-critic (SAC) algorithm can be derived by slight modifications of off-policy MDPO. Overall, MDPO is derived from the MD principles, offers a unified approach to viewing a number of popular RL algorithms, and performs better than or on-par with TRPO, PPO, and SAC in a number of continuous control tasks. Code is available at \url{https://github.com/manantomar/Mirror-Descent-Policy-Optimization}.

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Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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    Unregularized PMD with any constant step size converges to a limiting optimal policy for general decomposable Legendre mirror maps, with behavior governed by differentiability of ψ at 0 and 1.

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  3. Randomized Advantage Transformation (RAT): Computing Natural Policy Gradients via Direct Backpropagation

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  4. Post Reasoning: Improving the Performance of Non-Thinking Models at No Cost

    cs.AI 2026-05 conditional novelty 7.0

    Post-Reasoning boosts LLM accuracy by reversing the usual answer-after-reasoning order, delivering mean relative gains of 17.37% across 117 model-benchmark pairs with zero extra cost.

  5. Mirror Descent-Ascent for mean-field min-max problems

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    Establishes O(N^{-1/2}) convergence for simultaneous MDA and O(N^{-2/3}) for alternating MDA to mixed Nash equilibria in mean-field convex-concave min-max problems via dual-space Bregman analysis.

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  8. Listwise Policy Optimization: Group-based RLVR as Target-Projection on the LLM Response Simplex

    cs.LG 2026-05 unverdicted novelty 6.0

    Listwise Policy Optimization explicitly performs target-projection on the LLM response simplex, unifying and improving group-based RLVR methods with monotonic improvement and flexible divergences.

  9. Reinforcement Learning with Discrete Diffusion Policies for Combinatorial Action Spaces

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    Muon optimizer with weight decay and update scaling achieves ~2x efficiency over AdamW for large LLMs, shown via the Moonlight 3B/16B MoE model trained on 5.7T tokens.

  12. A Single Diffusion-Policy Controller for Multi-Task Block Pushing with Zero-Shot Sim-to-Real Transfer

    cs.RO 2026-07 conditional novelty 5.0

    One diffusion policy trained via energy-guided RL solves multi-shape block pushing without demos and transfers zero-shot to real robots under varied conditions.

  13. Randomized Advantage Transformation (RAT): Computing Natural Policy Gradients via Direct Backpropagation

    cs.LG 2026-05 conditional novelty 5.0

    RAT estimates Tikhonov-regularized natural policy gradients by rewriting them with the Woodbury identity, approximating the transformed advantage via randomized block Kaczmarz, and applying it as a vanilla policy grad...

  14. Optimal Posterior Sampling for Policy Identification in Tabular Markov Decision Processes

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