arXiv subjects

Benjamin Van Roy

Publications and source records attributed to Benjamin Van Roy.

At least 73 records · Page 4Linked to original sources

arXiv2021

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.

cs.LG↗

arXiv2021

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.

cs.LG↗

arXiv2021

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 presented algorithm achieves deep exploration. We also offer some intuition to how Langevin DQN achieves deep exploration. In addition, we present a modification of the Langevin DQN algorithm to improve the computational efficiency.

cs.LG↗

arXiv2021

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.

cs.LG↗

arXiv2020

A Tutorial on Thompson Sampling

Thompson sampling is an algorithm for online decision problems where actions are taken sequentially in a manner that must balance between exploiting what is known to maximize immediate performance and investing to accumulate new information that may improve future performance. The algorithm addresses a broad range of problems in a computationally efficient manner and is therefore enjoying wide use. This tutorial covers the algorithm and its application, illustrating concepts through a range of examples, including Bernoulli bandit problems, shortest path problems, product recommendation, assortment, active learning with neural networks, and reinforcement learning in Markov decision processes. Most of these problems involve complex information structures, where information revealed by taking an action informs beliefs about other actions. We will also discuss when and why Thompson sampling is or is not effective and relations to alternative algorithms.

cs.LG↗

arXiv2020

An Information-Theoretic Analysis for Thompson Sampling with Many Actions

Information-theoretic Bayesian regret bounds of Russo and Van Roy capture the dependence of regret on prior uncertainty. However, this dependence is through entropy, which can become arbitrarily large as the number of actions increases. We establish new bounds that depend instead on a notion of rate-distortion. Among other things, this allows us to recover through information-theoretic arguments a near-optimal bound for the linear bandit. We also offer a bound for the logistic bandit that dramatically improves on the best previously available, though this bound depends on an information-theoretic statistic that we have only been able to quantify via computation.

stat.ML↗

arXiv2020

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.

cs.LG↗

arXiv2020

Provably Efficient Reinforcement Learning with Aggregated States

We establish that an optimistic variant of Q-learning applied to a fixed-horizon episodic Markov decision process with an aggregated state representation incurs regret $\tilde{\mathcal{O}}(\sqrt{H^5 M K} + εHK)$, where $H$ is the horizon, $M$ is the number of aggregate states, $K$ is the number of episodes, and $ε$ is the largest difference between any pair of optimal state-action values associated with a common aggregate state. Notably, this regret bound does not depend on the number of states or actions and indicates that asymptotic per-period regret is no greater than $ε$, independent of horizon. To our knowledge, this is the first such result that applies to reinforcement learning with nontrivial value function approximation without any restrictions on transition probabilities.

stat.ML↗

arXiv2020

Behaviour Suite for Reinforcement Learning

This paper introduces the Behaviour Suite for Reinforcement Learning, or bsuite for short. bsuite is a collection of carefully-designed experiments that investigate core capabilities of reinforcement learning (RL) agents with two objectives. First, to collect clear, informative and scalable problems that capture key issues in the design of general and efficient learning algorithms. Second, to study agent behaviour through their performance on these shared benchmarks. To complement this effort, we open source github.com/deepmind/bsuite, which automates evaluation and analysis of any agent on bsuite. This library facilitates reproducible and accessible research on the core issues in RL, and ultimately the design of superior learning algorithms. Our code is Python, and easy to use within existing projects. We include examples with OpenAI Baselines, Dopamine as well as new reference implementations. Going forward, we hope to incorporate more excellent experiments from the research community, and commit to a periodic review of bsuite from a committee of prominent researchers.

cs.LG↗

arXiv2020

Satisficing in Time-Sensitive Bandit Learning

Much of the recent literature on bandit learning focuses on algorithms that aim to converge on an optimal action. One shortcoming is that this orientation does not account for time sensitivity, which can play a crucial role when learning an optimal action requires much more information than near-optimal ones. Indeed, popular approaches such as upper-confidence-bound methods and Thompson sampling can fare poorly in such situations. We consider instead learning a satisficing action, which is near-optimal while requiring less information, and propose satisficing Thompson sampling, an algorithm that serves this purpose. We establish a general bound on expected discounted regret and study the application of satisficing Thompson sampling to linear and infinite-armed bandits, demonstrating arbitrarily large benefits over Thompson sampling. We also discuss the relation between the notion of satisficing and the theory of rate distortion, which offers guidance on the selection of satisficing actions.

cs.LG↗

arXiv2019

Information-Theoretic Confidence Bounds for Reinforcement Learning

We integrate information-theoretic concepts into the design and analysis of optimistic algorithms and Thompson sampling. By making a connection between information-theoretic quantities and confidence bounds, we obtain results that relate the per-period performance of the agent with its information gain about the environment, thus explicitly characterizing the exploration-exploitation tradeoff. The resulting cumulative regret bound depends on the agent's uncertainty over the environment and quantifies the value of prior information. We show applicability of this approach to several environments, including linear bandits, tabular MDPs, and factored MDPs. These examples demonstrate the potential of a general information-theoretic approach for the design and analysis of reinforcement learning algorithms.

stat.ML↗

arXiv2019

Comments on the Du-Kakade-Wang-Yang Lower Bounds

Du, Kakade, Wang, and Yang recently established intriguing lower bounds on sample complexity, which suggest that reinforcement learning with a misspecified representation is intractable. Another line of work, which centers around a statistic called the eluder dimension, establishes tractability of problems similar to those considered in the Du-Kakade-Wang-Yang paper. We compare these results and reconcile interpretations.

cs.LG↗

arXiv2019

Deep Exploration via Randomized Value Functions

We study the use of randomized value functions to guide deep exploration in reinforcement learning. This offers an elegant means for synthesizing statistically and computationally efficient exploration with common practical approaches to value function learning. We present several reinforcement learning algorithms that leverage randomized value functions and demonstrate their efficacy through computational studies. We also prove a regret bound that establishes statistical efficiency with a tabular representation.

stat.ML↗

arXiv2019

On the Performance of Thompson Sampling on Logistic Bandits

We study the logistic bandit, in which rewards are binary with success probability $\exp(βa^\top θ) / (1 + \exp(βa^\top θ))$ and actions $a$ and coefficients $θ$ are within the $d$-dimensional unit ball. While prior regret bounds for algorithms that address the logistic bandit exhibit exponential dependence on the slope parameter $β$, we establish a regret bound for Thompson sampling that is independent of $β$. Specifically, we establish that, when the set of feasible actions is identical to the set of possible coefficient vectors, the Bayesian regret of Thompson sampling is $\tilde{O}(d\sqrt{T})$. We also establish a $\tilde{O}(\sqrt{dηT}/λ)$ bound that applies more broadly, where $λ$ is the worst-case optimal log-odds and $η$ is the "fragility dimension," a new statistic we define to capture the degree to which an optimal action for one model fails to satisfice for others. We demonstrate that the fragility dimension plays an essential role by showing that, for any $ε> 0$, no algorithm can achieve $\mathrm{poly}(d, 1/λ)\cdot T^{1-ε}$ regret.

stat.ML↗

arXiv2018

Scalable Coordinated Exploration in Concurrent Reinforcement Learning

We consider a team of reinforcement learning agents that concurrently operate in a common environment, and we develop an approach to efficient coordinated exploration that is suitable for problems of practical scale. Our approach builds on seed sampling (Dimakopoulou and Van Roy, 2018) and randomized value function learning (Osband et al., 2016). We demonstrate that, for simple tabular contexts, the approach is competitive with previously proposed tabular model learning methods (Dimakopoulou and Van Roy, 2018). With a higher-dimensional problem and a neural network value function representation, the approach learns quickly with far fewer agents than alternative exploration schemes.

cs.LG↗

arXiv2018

Gaussian-Dirichlet Posterior Dominance in Sequential Learning

We consider the problem of sequential learning from categorical observations bounded in [0,1]. We establish an ordering between the Dirichlet posterior over categorical outcomes and a Gaussian posterior under observations with N(0,1) noise. We establish that, conditioned upon identical data with at least two observations, the posterior mean of the categorical distribution will always second-order stochastically dominate the posterior mean of the Gaussian distribution. These results provide a useful tool for the analysis of sequential learning under categorical outcomes.

stat.ML↗

arXiv2018

Coordinated Exploration in Concurrent Reinforcement Learning

We consider a team of reinforcement learning agents that concurrently learn to operate in a common environment. We identify three properties - adaptivity, commitment, and diversity - which are necessary for efficient coordinated exploration and demonstrate that straightforward extensions to single-agent optimistic and posterior sampling approaches fail to satisfy them. As an alternative, we propose seed sampling, which extends posterior sampling in a manner that meets these requirements. Simulation results investigate how per-agent regret decreases as the number of agents grows, establishing substantial advantages of seed sampling over alternative exploration schemes.

cs.AI↗

arXiv2017

Learning to Price with Reference Effects

As a firm varies the price of a product, consumers exhibit reference effects, making purchase decisions based not only on the prevailing price but also the product's price history. We consider the problem of learning such behavioral patterns as a monopolist releases, markets, and prices products. This context calls for pricing decisions that intelligently trade off between maximizing revenue generated by a current product and probing to gain information for future benefit. Due to dependence on price history, realized demand can reflect delayed consequences of earlier pricing decisions. As such, inference entails attribution of outcomes to prior decisions and effective exploration requires planning price sequences that yield informative future outcomes. Despite the considerable complexity of this problem, we offer a tractable systematic approach. In particular, we frame the problem as one of reinforcement learning and leverage Thompson sampling. We also establish a regret bound that provides graceful guarantees on how performance improves as data is gathered and how this depends on the complexity of the demand model. We illustrate merits of the approach through simulations.

cs.GT↗