Why is Posterior Sampling Better than Optimism for Reinforcement Learning?

By Ian Osband, Benjamin Van Roy. 2016

289 citations recorded by the source corpus.

Computational results demonstrate that posterior sampling for reinforcement learning (PSRL) dramatically outperforms algorithms driven by optimism, such as UCRL2. We provide insight into the extent of this performance boost and the phenomenon that drives it. We leverage this insight to establish an $\tilde{O}(H\sqrt{SAT})$ Bayesian expected regret bound for PSRL in finite-horizon episodic Markov decision processes, where $H$ is the horizon, $S$ is the number of states, $A$ is the number of actions and $T$ is the time elapsed. This improves upon the best previous bound of $\tilde{O}(H S \sqrt{AT})$ for any reinforcement learning algorithm.

Subfields: Artificial Intelligence, Management Science and Operations Research, Reinforcement Learning

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Citations in the corpus

Shaking the foundations: delusions in sequence models for interaction and control (2021, background): “In addition, the resulting policy is adaptive—essentially, it is Thompson sampling—and will converge to the expert’s policy under broad conditions [12, 14, 16].”
Neural Approaches to Conversational AI (2018, neutral): “in the hope of discovering a better policy in the long run (e.g., Daubigney et al., 2011). While exploration in ﬁnite-state RL is relatively well-understood (Strehl et al., 2009; Jaksch et al., 2010; Osband and Roy, 2017; Dann et al., 2017), exploration when parametric models like neural networks ar”
Offline Reinforcement Learning: Tutorial, Review, and Perspectives on Open Problems (2020, background): “In exploration, acting optimistically with respect to estimated uncertainty, or utilizing posterior sampling, has been shown to be effective in practice (Osband and Van Roy, 2017).”
Conservative Q-Learning for Offline Reinforcement Learning (2020, methodology): “Alternate prior approaches to offline RL estimate some sort of uncertainty to determine the trustworthiness of a Q-value prediction [30, 3, 34], typically using uncertainty estimation techniques from exploration in online RL [47, 26, 46, 7].”
COMBO: Conservative Offline Model-Based Policy Optimization (2021, methodology): “Following prior work [42, 19, 29], we assume: Assumption A1.”
Randomized Prior Functions for Deep Reinforcement Learning (2018, background): “Further, this empirical scaling matches that predicted by the regret bound tabular domain [51] (see Figure 8).”
Deep Exploration via Randomized Value Functions (2017, background): “However, recent work suggests that this bound is loose [37], and the associated plot in Figure 5 strengthens the case for that hypothesis.”
Regret Minimization for Reinforcement Learning by Evaluating the Optimal Bias Function (2019, background): “There are also considerable works devoted to study ﬁnite-horizon MDP. Osband and Van Roy [2016] presented PRSL to establish a Bayesian regret bound of ˜ O ( H √ SAT ) using posterior sampling method.”
Bayesian Inference for Large Scale Image Classification (2019, background): “Bayesian inference can also be applied to differential privacy, where each individual sample has increased privacy guarantees [2], and to reinforcement learning, where one can leverage model uncertainty to balance between exploration and exploitation [3].”
Bandit Algorithms (2020, methodology): “[1971], while a more modern text is by Peskir and Shiryaev [2006], which includes a proof of Theorem 35.”