Reinforcement Learning, Bit by Bit

Reinforcement learning agents have demonstrated remarkable achievements in simulated environments. Data efficiency poses an impediment to carrying this success over to real environments. The design of data-efficient agents calls for a deeper understanding of information acquisition and representation. We develop concepts and establish a regret bound that together offer principled guidance. The bound sheds light on questions of what information to seek, how to seek that information, and it what information to retain. To illustrate concepts, we design simple agents that build on them and present computational results that demonstrate improvements in data efficiency.

Simple Agent, Complex Environment: Efficient Reinforcement Learning with Agent State

We design a simple reinforcement learning agent that, with a specification only of agent state dynamics and a reward function, can operate with some degree of competence in any environment. The agent maintains only visitation counts and value estimates for each agent-state-action pair. The value function is updated incrementally in response to temporal differences and optimistic boosts that encourage exploration. The agent executes actions that are greedy with respect to this value function. We establish a regret bound demonstrating convergence to near-optimal per-period performance, where the time taken to achieve near-optimality is polynomial in the number of agent states and actions, as well as the reward mixing time of the best policy within the reference policy class, which is comprised of those that depend on history only through agent state. Notably, there is no further dependence on the number of environment states or mixing times associated with other policies or statistics of history. Our result sheds light on the potential benefits of (deep) representation learning, which has demonstrated the capability to extract compact and relevant features from high-dimensional interaction histories.

A Bit Better? Quantifying Information for Bandit Learning

The information ratio offers an approach to assessing the efficacy with which an agent balances between exploration and exploitation. Originally, this was defined to be the ratio between squared expected regret and the mutual information between the environment and action-observation pair, which represents a measure of information gain. Recent work has inspired consideration of alternative information measures, particularly for use in analysis of bandit learning algorithms to arrive at tighter regret bounds. We investigate whether quantification of information via such alternatives can improve the realized performance of information-directed sampling, which aims to minimize the information ratio.

Deciding What to Learn: A Rate-Distortion Approach

Agents that learn to select optimal actions represent a prominent focus of the sequential decision-making literature. In the face of a complex environment or constraints on time and resources, however, aiming to synthesize such an optimal policy can become infeasible. These scenarios give rise to an important trade-off between the information an agent must acquire to learn and the sub-optimality of the resulting policy. While an agent designer has a preference for how this trade-off is resolved, existing approaches further require that the designer translate these preferences into a fixed learning target for the agent. In this work, leveraging rate-distortion theory, we automate this process such that the designer need only express their preferences via a single hyperparameter and the agent is endowed with the ability to compute its own learning targets that best achieve the desired trade-off. We establish a general bound on expected discounted regret for an agent that decides what to learn in this manner along with computational experiments that illustrate the expressiveness of designer preferences and even show improvements over Thompson sampling in identifying an optimal policy.

Randomized Value Functions via Posterior State-Abstraction Sampling

State abstraction has been an essential tool for dramatically improving the sample efficiency of reinforcement-learning algorithms. Indeed, by exposing and accentuating various types of latent structure within the environment, different classes of state abstraction have enabled improved theoretical guarantees and empirical performance. When dealing with state abstractions that capture structure in the value function, however, a standard assumption is that the true abstraction has been supplied or unrealistically computed a priori, leaving open the question of how to efficiently uncover such latent structure while jointly seeking out optimal behavior. Taking inspiration from the bandit literature, we propose that an agent seeking out latent task structure must explicitly represent and maintain its uncertainty over that structure as part of its overall uncertainty about the environment. We introduce a practical algorithm for doing this using two posterior distributions over state abstractions and abstract-state values. In empirically validating our approach, we find that substantial performance gains lie in the multi-task setting where tasks share a common, low-dimensional representation.

Hypermodels for Exploration

We study the use of hypermodels to represent epistemic uncertainty and guide exploration. This generalizes and extends the use of ensembles to approximate Thompson sampling. The computational cost of training an ensemble grows with its size, and as such, prior work has typically been limited to ensembles with tens of elements. We show that alternative hypermodels can enjoy dramatic efficiency gains, enabling behavior that would otherwise require hundreds or thousands of elements, and even succeed in situations where ensemble methods fail to learn regardless of size. This allows more accurate approximation of Thompson sampling as well as use of more sophisticated exploration schemes. In particular, we consider an approximate form of information-directed sampling and demonstrate performance gains relative to Thompson sampling. As alternatives to ensembles, we consider linear and neural network hypermodels, also known as hypernetworks. We prove that, with neural network base models, a linear hypermodel can represent essentially any distribution over functions, and as such, hypernetworks are no more expressive.

Langevin DQN

Algorithms that tackle deep exploration -- an important challenge in reinforcement learning -- have relied on epistemic uncertainty representation through ensembles or other hypermodels, exploration bonuses, or visitation count distributions. An open question is whether deep exploration can be achieved by an incremental reinforcement learning algorithm that tracks a single point estimate, without additional complexity required to account for epistemic uncertainty. We answer this question in the affirmative. In particular, we develop Langevin DQN, a variation of DQN that differs only in perturbing parameter updates with Gaussian noise, and demonstrate through a computational study that the algorithm achieves deep exploration. We also provide an intuition for why Langevin DQN performs deep exploration.