arXiv subjects

Ian Osband

Publications and source records attributed to Ian Osband.

At least 37 records · Page 2Linked to original sources

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

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

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↗

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

Meta-learning of Sequential Strategies

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains. To do so, we present basic algorithmic templates for building near-optimal predictors and reinforcement learners which behave as if they had a probabilistic model that allowed them to efficiently exploit task structure. Furthermore, we recast memory-based meta-learning within a Bayesian framework, showing that the meta-learned strategies are near-optimal because they amortize Bayes-filtered data, where the adaptation is implemented in the memory dynamics as a state-machine of sufficient statistics. Essentially, memory-based meta-learning translates the hard problem of probabilistic sequential inference into a regression problem.

cs.LG↗

arXiv2019

Noisy Networks for Exploration

We introduce NoisyNet, a deep reinforcement learning agent with parametric noise added to its weights, and show that the induced stochasticity of the agent's policy can be used to aid efficient exploration. The parameters of the noise are learned with gradient descent along with the remaining network weights. NoisyNet is straightforward to implement and adds little computational overhead. We find that replacing the conventional exploration heuristics for A3C, DQN and dueling agents (entropy reward and $ε$-greedy respectively) with NoisyNet yields substantially higher scores for a wide range of Atari games, in some cases advancing the agent from sub to super-human performance.

cs.LG↗

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

Randomized Prior Functions for Deep Reinforcement Learning

Dealing with uncertainty is essential for efficient reinforcement learning. There is a growing literature on uncertainty estimation for deep learning from fixed datasets, but many of the most popular approaches are poorly-suited to sequential decision problems. Other methods, such as bootstrap sampling, have no mechanism for uncertainty that does not come from the observed data. We highlight why this can be a crucial shortcoming and propose a simple remedy through addition of a randomized untrainable `prior' network to each ensemble member. We prove that this approach is efficient with linear representations, provide simple illustrations of its efficacy with nonlinear representations and show that this approach scales to large-scale problems far better than previous attempts.

stat.ML↗

arXiv2018

The Uncertainty Bellman Equation and Exploration

We consider the exploration/exploitation problem in reinforcement learning. For exploitation, it is well known that the Bellman equation connects the value at any time-step to the expected value at subsequent time-steps. In this paper we consider a similar \textit{uncertainty} Bellman equation (UBE), which connects the uncertainty at any time-step to the expected uncertainties at subsequent time-steps, thereby extending the potential exploratory benefit of a policy beyond individual time-steps. We prove that the unique fixed point of the UBE yields an upper bound on the variance of the posterior distribution of the Q-values induced by any policy. This bound can be much tighter than traditional count-based bonuses that compound standard deviation rather than variance. Importantly, and unlike several existing approaches to optimism, this method scales naturally to large systems with complex generalization. Substituting our UBE-exploration strategy for $ε$-greedy improves DQN performance on 51 out of 57 games in the Atari suite.

cs.AI↗

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↗

arXiv2017

Deep Q-learning from Demonstrations

Deep reinforcement learning (RL) has achieved several high profile successes in difficult decision-making problems. However, these algorithms typically require a huge amount of data before they reach reasonable performance. In fact, their performance during learning can be extremely poor. This may be acceptable for a simulator, but it severely limits the applicability of deep RL to many real-world tasks, where the agent must learn in the real environment. In this paper we study a setting where the agent may access data from previous control of the system. We present an algorithm, Deep Q-learning from Demonstrations (DQfD), that leverages small sets of demonstration data to massively accelerate the learning process even from relatively small amounts of demonstration data and is able to automatically assess the necessary ratio of demonstration data while learning thanks to a prioritized replay mechanism. DQfD works by combining temporal difference updates with supervised classification of the demonstrator's actions. We show that DQfD has better initial performance than Prioritized Dueling Double Deep Q-Networks (PDD DQN) as it starts with better scores on the first million steps on 41 of 42 games and on average it takes PDD DQN 83 million steps to catch up to DQfD's performance. DQfD learns to out-perform the best demonstration given in 14 of 42 games. In addition, DQfD leverages human demonstrations to achieve state-of-the-art results for 11 games. Finally, we show that DQfD performs better than three related algorithms for incorporating demonstration data into DQN.

cs.AI↗

arXiv2017

Minimax Regret Bounds for Reinforcement Learning

We consider the problem of provably optimal exploration in reinforcement learning for finite horizon MDPs. We show that an optimistic modification to value iteration achieves a regret bound of $\tilde{O}( \sqrt{HSAT} + H^2S^2A+H\sqrt{T})$ where $H$ is the time horizon, $S$ the number of states, $A$ the number of actions and $T$ the number of time-steps. This result improves over the best previous known bound $\tilde{O}(HS \sqrt{AT})$ achieved by the UCRL2 algorithm of Jaksch et al., 2010. The key significance of our new results is that when $T\geq H^3S^3A$ and $SA\geq H$, it leads to a regret of $\tilde{O}(\sqrt{HSAT})$ that matches the established lower bound of $Ω(\sqrt{HSAT})$ up to a logarithmic factor. Our analysis contains two key insights. We use careful application of concentration inequalities to the optimal value function as a whole, rather than to the transitions probabilities (to improve scaling in $S$), and we define Bernstein-based "exploration bonuses" that use the empirical variance of the estimated values at the next states (to improve scaling in $H$).

stat.ML↗

arXiv2017

Why is Posterior Sampling Better than Optimism for Reinforcement Learning?

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.

stat.ML↗

arXiv2017

On Optimistic versus Randomized Exploration in Reinforcement Learning

We discuss the relative merits of optimistic and randomized approaches to exploration in reinforcement learning. Optimistic approaches presented in the literature apply an optimistic boost to the value estimate at each state-action pair and select actions that are greedy with respect to the resulting optimistic value function. Randomized approaches sample from among statistically plausible value functions and select actions that are greedy with respect to the random sample. Prior computational experience suggests that randomized approaches can lead to far more statistically efficient learning. We present two simple analytic examples that elucidate why this is the case. In principle, there should be optimistic approaches that fare well relative to randomized approaches, but that would require intractable computation. Optimistic approaches that have been proposed in the literature sacrifice statistical efficiency for the sake of computational efficiency. Randomized approaches, on the other hand, may enable simultaneous statistical and computational efficiency.

stat.ML↗

arXiv2016

Posterior Sampling for Reinforcement Learning Without Episodes

This is a brief technical note to clarify some of the issues with applying the application of the algorithm posterior sampling for reinforcement learning (PSRL) in environments without fixed episodes. In particular, this paper aims to: - Review some of results which have been proven for finite horizon MDPs (Osband et al 2013, 2014a, 2014b, 2016) and also for MDPs with finite ergodic structure (Gopalan et al 2014). - Review similar results for optimistic algorithms in infinite horizon problems (Jaksch et al 2010, Bartlett and Tewari 2009, Abbasi-Yadkori and Szepesvari 2011), with particular attention to the dynamic episode growth. - Highlight the delicate technical issue which has led to a fault in the proof of the lazy-PSRL algorithm (Abbasi-Yadkori and Szepesvari 2015). We present an explicit counterexample to this style of argument. Therefore, we suggest that the Theorem 2 in (Abbasi-Yadkori and Szepesvari 2015) be instead considered a conjecture, as it has no rigorous proof. - Present pragmatic approaches to apply PSRL in infinite horizon problems. We conjecture that, under some additional assumptions, it will be possible to obtain bounds $O( \sqrt{T} )$ even without episodic reset. We hope that this note serves to clarify existing results in the field of reinforcement learning and provides interesting motivation for future work.

stat.ML↗

arXiv2016

On Lower Bounds for Regret in Reinforcement Learning

This is a brief technical note to clarify the state of lower bounds on regret for reinforcement learning. In particular, this paper: - Reproduces a lower bound on regret for reinforcement learning, similar to the result of Theorem 5 in the journal UCRL2 paper (Jaksch et al 2010). - Clarifies that the proposed proof of Theorem 6 in the REGAL paper (Bartlett and Tewari 2009) does not hold using the standard techniques without further work. We suggest that this result should instead be considered a conjecture as it has no rigorous proof. - Suggests that the conjectured lower bound given by (Bartlett and Tewari 2009) is incorrect and, in fact, it is possible to improve the scaling of the upper bound to match the weaker lower bounds presented in this paper. We hope that this note serves to clarify existing results in the field of reinforcement learning and provides interesting motivation for future work.

stat.ML↗

arXiv2016

Deep Exploration via Bootstrapped DQN

Efficient exploration in complex environments remains a major challenge for reinforcement learning. We propose bootstrapped DQN, a simple algorithm that explores in a computationally and statistically efficient manner through use of randomized value functions. Unlike dithering strategies such as epsilon-greedy exploration, bootstrapped DQN carries out temporally-extended (or deep) exploration; this can lead to exponentially faster learning. We demonstrate these benefits in complex stochastic MDPs and in the large-scale Arcade Learning Environment. Bootstrapped DQN substantially improves learning times and performance across most Atari games.

cs.LG↗

arXiv2016

Generalization and Exploration via Randomized Value Functions

We propose randomized least-squares value iteration (RLSVI) -- a new reinforcement learning algorithm designed to explore and generalize efficiently via linearly parameterized value functions. We explain why versions of least-squares value iteration that use Boltzmann or epsilon-greedy exploration can be highly inefficient, and we present computational results that demonstrate dramatic efficiency gains enjoyed by RLSVI. Further, we establish an upper bound on the expected regret of RLSVI that demonstrates near-optimality in a tabula rasa learning context. More broadly, our results suggest that randomized value functions offer a promising approach to tackling a critical challenge in reinforcement learning: synthesizing efficient exploration and effective generalization.

stat.ML↗