Rethinking the Discount Factor in Reinforcement Learning: A Decision Theoretic Approach

Reinforcement learning (RL) agents have traditionally been tasked with maximizing the value function of a Markov decision process (MDP), either in continuous settings, with fixed discount factor $\gamma < 1$, or in episodic settings, with $\gamma = 1$. While this has proven effective for specific tasks with well-defined objectives (e.g., games), it has never been established that fixed discounting is suitable for general purpose use (e.g., as a model of human preferences). This paper characterizes rationality in sequential decision making using a set of seven axioms and arrives at a form of discounting that generalizes traditional fixed discounting. In particular, our framework admits a state-action dependent "discount" factor that is not constrained to be less than 1, so long as there is eventual long run discounting. Although this broadens the range of possible preference structures in continuous settings, we show that there exists a unique "optimizing MDP" with fixed $\gamma < 1$ whose optimal value function matches the true utility of the optimal policy, and we quantify the difference between value and utility for suboptimal policies. Our work can be seen as providing a normative justification for (a slight generalization of) Martha White's RL task formalism (2017) and other recent departures from the traditional RL, and is relevant to task specification in RL, inverse RL and preference-based RL.Comment: 8 pages + 1 page supplement. In proceedings of AAAI 2019. Slides, poster and bibtex available at https://silviupitis.com/#rethinking-the-discount-factor-in-reinforcement-learning-a-decision-theoretic-approac

Bayesian Exploration Networks

Bayesian reinforcement learning (RL) offers a principled and elegant approach for sequential decision making under uncertainty. Most notably, Bayesian agents do not face an exploration/exploitation dilemma, a major pathology of frequentist methods. A key challenge for Bayesian RL is the computational complexity of learning Bayes-optimal policies, which is only tractable in toy domains. In this paper we propose a novel model-free approach to address this challenge. Rather than modelling uncertainty in high-dimensional state transition distributions as model-based approaches do, we model uncertainty in a one-dimensional Bellman operator. Our theoretical analysis reveals that existing model-free approaches either do not propagate epistemic uncertainty through the MDP or optimise over a set of contextual policies instead of all history-conditioned policies. Both approximations yield policies that can be arbitrarily Bayes-suboptimal. To overcome these issues, we introduce the Bayesian exploration network (BEN) which uses normalising flows to model both the aleatoric uncertainty (via density estimation) and epistemic uncertainty (via variational inference) in the Bellman operator. In the limit of complete optimisation, BEN learns true Bayes-optimal policies, but like in variational expectation-maximisation, partial optimisation renders our approach tractable. Empirical results demonstrate that BEN can learn true Bayes-optimal policies in tasks where existing model-free approaches fail

Exploration via Elliptical Episodic Bonuses

In recent years, a number of reinforcement learning (RL) methods have been proposed to explore complex environments which differ across episodes. In this work, we show that the effectiveness of these methods critically relies on a count-based episodic term in their exploration bonus. As a result, despite their success in relatively simple, noise-free settings, these methods fall short in more realistic scenarios where the state space is vast and prone to noise. To address this limitation, we introduce Exploration via Elliptical Episodic Bonuses (E3B), a new method which extends count-based episodic bonuses to continuous state spaces and encourages an agent to explore states that are diverse under a learned embedding within each episode. The embedding is learned using an inverse dynamics model in order to capture controllable aspects of the environment. Our method sets a new state-of-the-art across 16 challenging tasks from the MiniHack suite, without requiring task-specific inductive biases. E3B also matches existing methods on sparse reward, pixel-based Vizdoom environments, and outperforms existing methods in reward-free exploration on Habitat, demonstrating that it can scale to high-dimensional pixel-based observations and realistic environments