# Provably Efficient Reinforcement Learning for Discounted MDPs with Feature Mapping

arXiv: https://arxiv.org/abs/2006.13165 · HTML: https://mlsanity.com/paper/2006.13165/

## Key facts

- Cited by 102 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

## Built on by (most cited first, 30 of 102)

- [Provably Efficient Reinforcement Learning with Linear Function Approximation Under Adaptivity Constraints](https://mlsanity.com/paper/2101.02195/) (2021)
- [Human-in-the-loop: Provably Efficient Preference-based Reinforcement Learning with General Function Approximation](https://mlsanity.com/paper/2205.11140/) (2022)
- [Near-optimal Offline Reinforcement Learning with Linear Representation: Leveraging Variance Information with Pessimism](https://mlsanity.com/paper/2203.05804/) (2022)
- [Unpacking Reward Shaping: Understanding the Benefits of Reward Engineering on Sample Complexity](https://mlsanity.com/paper/2210.09579/) (2022)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes](https://mlsanity.com/paper/2212.06132/) (2022)
- [Cautiously Optimistic Policy Optimization and Exploration with Linear Function Approximation](https://mlsanity.com/paper/2103.12923/) (2021)
- [Computationally Efficient Horizon-Free Reinforcement Learning for Linear Mixture MDPs](https://mlsanity.com/paper/2205.11507/) (2022)
- [Reward-Free RL is No Harder Than Reward-Aware RL in Linear Markov Decision Processes](https://mlsanity.com/paper/2201.11206/) (2022)
- [Reason for Future, Act for Now: A Principled Framework for Autonomous LLM Agents with Provable Sample Efficiency](https://mlsanity.com/paper/2309.17382/) (2023)
- [Improved Variance-Aware Confidence Sets for Linear Bandits and Linear Mixture MDP](https://mlsanity.com/paper/2101.12745/) (2021)
- [Near-optimal Representation Learning for Linear Bandits and Linear RL](https://mlsanity.com/paper/2102.04132/) (2021)
- [Leveraging Offline Data in Online Reinforcement Learning](https://mlsanity.com/paper/2211.04974/) (2022)
- [An Exponential Lower Bound for Linearly-Realizable MDPs with Constant Suboptimality Gap](https://mlsanity.com/paper/2103.12690/) (2021)
- [MADE: Exploration via Maximizing Deviation from Explored Regions](https://mlsanity.com/paper/2106.10268/) (2021)
- [Variance-Dependent Regret Bounds for Linear Bandits and Reinforcement Learning: Adaptivity and Computational Efficiency](https://mlsanity.com/paper/2302.10371/) (2023)
- [First-Order Regret in Reinforcement Learning with Linear Function Approximation: A Robust Estimation Approach](https://mlsanity.com/paper/2112.03432/) (2021)
- [Variance-Aware Off-Policy Evaluation with Linear Function Approximation](https://mlsanity.com/paper/2106.11960/) (2021)
- [Instance-Dependent Near-Optimal Policy Identification in Linear MDPs via Online Experiment Design](https://mlsanity.com/paper/2207.02575/) (2022)
- [Target Network and Truncation Overcome The Deadly Triad in Q-Learning](https://mlsanity.com/paper/2203.02628/) (2022)
- [Provably Efficient Model-Free Constrained RL with Linear Function Approximation](https://mlsanity.com/paper/2206.11889/) (2022)
- [A General Framework for Sample-Efficient Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/2209.15634/) (2022)
- [Robust Policy Gradient against Strong Data Corruption](https://mlsanity.com/paper/2102.05800/) (2021)
- [Reward-Free Model-Based Reinforcement Learning with Linear Function Approximation](https://mlsanity.com/paper/2110.06394/) (2021)
- [A Theoretical Analysis of Optimistic Proximal Policy Optimization in Linear Markov Decision Processes](https://mlsanity.com/paper/2305.08841/) (2023)
- [Near-optimal Policy Optimization Algorithms for Learning Adversarial Linear Mixture MDPs](https://mlsanity.com/paper/2102.08940/) (2021)
- [Contrastive UCB: Provably Efficient Contrastive Self-Supervised Learning in Online Reinforcement Learning](https://mlsanity.com/paper/2207.14800/) (2022)
- [Almost Optimal Algorithms for Two-player Zero-Sum Linear Mixture Markov Games](https://mlsanity.com/paper/2102.07404/) (2021)
- [Sparse Feature Selection Makes Batch Reinforcement Learning More Sample Efficient](https://mlsanity.com/paper/2011.04019/) (2020)
- [Efficient Local Planning with Linear Function Approximation](https://mlsanity.com/paper/2108.05533/) (2021)
- [Learning Stochastic Shortest Path with Linear Function Approximation](https://mlsanity.com/paper/2110.12727/) (2021)

## Abstract (arXiv)

Modern tasks in reinforcement learning have large state and action spaces. To deal with them efficiently, one often uses predefined feature mapping to represent states and actions in a low-dimensional space. In this paper, we study reinforcement learning for discounted Markov Decision Processes (MDPs), where the transition kernel can be parameterized as a linear function of certain feature mapping. We propose a novel algorithm that makes use of the feature mapping and obtains a tilde O(d√T/(1-γ)2) regret, where d is the dimension of the feature space, T is the time horizon and γ is the discount factor of the MDP. To the best of our knowledge, this is the first polynomial regret bound without accessing the generative model or making strong assumptions such as ergodicity of the MDP. By constructing a special class of MDPs, we also show that for any algorithms, the regret is lower bounded by Omega(d√T/(1-γ)1.5). Our upper and lower bound results together suggest that the proposed reinforcement learning algorithm is near-optimal up to a (1-γ)-0.5 factor.