Model-Based Exploration in Monitored Markov Decision Processes

A tenet of reinforcement learning is that rewards are always observed by the agent. However, this is not true in many realistic settings, e.g., a human observer may not always be able to provide rewards, a sensor to observe rewards may be limited or broken, or rewards may be unavailable during deployment. Monitored Markov decision processes (Mon-MDPs) have recently been proposed as a model of such settings. Yet, Mon-MDP algorithms developed thus far do not fully exploit the problem structure, cannot take advantage of a known monitor, have no worst-case guarantees for ``unsolvable'' Mon-MDPs without specific initialization, and only have asymptotic proofs of convergence. This paper makes three contributions. First, we introduce a model-based algorithm for Mon-MDPs that addresses all of these shortcomings. The algorithm uses two instances of model-based interval estimation, one to guarantee that observable rewards are indeed observed, and another to learn the optimal policy. Second, empirical results demonstrate these advantages, showing faster convergence than prior algorithms in over two dozen benchmark settings, and even more dramatic improvements when the monitor process is known. Third, we present the first finite-sample bound on performance and show convergence to an optimal worst-case policy when some rewards are never observable.

Beyond Optimism: Exploration With Partially Observable Rewards

Exploration in reinforcement learning (RL) remains an open challenge. RL algorithms rely on observing rewards to train the agent, and if informative rewards are sparse the agent learns slowly or may not learn at all. To improve exploration and reward discovery, popular algorithms rely on optimism. But what if sometimes rewards are unobservable, e.g., situations of partial monitoring in bandits and the recent formalism of monitored Markov decision process? In this case, optimism can lead to suboptimal behavior that does not explore further to collapse uncertainty. With this paper, we present a novel exploration strategy that overcomes the limitations of existing methods and guarantees convergence to an optimal policy even when rewards are not always observable. We further propose a collection of tabular environments for benchmarking exploration in RL (with and without unobservable rewards) and show that our method outperforms existing ones.

Monitored Markov Decision Processes

In reinforcement learning (RL), an agent learns to perform a task by interacting with an environment and receiving feedback (a numerical reward) for its actions. However, the assumption that rewards are always observable is often not applicable in real-world problems. For example, the agent may need to ask a human to supervise its actions or activate a monitoring system to receive feedback. There may even be a period of time before rewards become observable, or a period of time after which rewards are no longer given. In other words, there are cases where the environment generates rewards in response to the agent's actions but the agent cannot observe them. In this paper, we formalize a novel but general RL framework - Monitored MDPs - where the agent cannot always observe rewards. We discuss the theoretical and practical consequences of this setting, show challenges raised even in toy environments, and propose algorithms to begin to tackle this novel setting. This paper introduces a powerful new formalism that encompasses both new and existing problems and lays the foundation for future research.