# PAC Reinforcement Learning with Rich Observations

arXiv: https://arxiv.org/abs/1602.02722 · HTML: https://mlsanity.com/paper/1602.02722/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2016.

## Built on by (most cited first, 4 of 4)

- [Learning Efficiently Function Approximation for Contextual MDP](https://mlsanity.com/paper/2203.00995/) (2022)
- [Congested Bandits: Optimal Routing via Short-term Resets](https://mlsanity.com/paper/2301.09251/) (2023)
- [Adaptive Estimation and Optimal Control in Offline Contextual MDPs without Stationarity](https://mlsanity.com/paper/2605.03393/) (2026)
- [Memoryless Policy Iteration for Episodic POMDPs](https://mlsanity.com/paper/2512.11082/) (2025)

## Abstract (arXiv)

We propose and study a new model for reinforcement learning with rich observations, generalizing contextual bandits to sequential decision making. These models require an agent to take actions based on observations (features) with the goal of achieving long-term performance competitive with a large set of policies. To avoid barriers to sample-efficient learning associated with large observation spaces and general POMDPs, we focus on problems that can be summarized by a small number of hidden states and have long-term rewards that are predictable by a reactive function class. In this setting, we design and analyze a new reinforcement learning algorithm, Least Squares Value Elimination by Exploration. We prove that the algorithm learns near optimal behavior after a number of episodes that is polynomial in all relevant parameters, logarithmic in the number of policies, and independent of the size of the observation space. Our result provides theoretical justification for reinforcement learning with function approximation.