Specifying a numeric reward function for reinforcement learning typically requires a lot of hand-tuning from a human expert. In contrast, preference-based reinforcement learning (PBRL) utilizes only pairwise comparisons between trajectories as a feedback signal, which are often more intuitive to specify. Currently available approaches to PBRL for control problems with continuous state/action spaces require a known or estimated model, which is often not available and hard to learn. In this paper, we integrate preference-based estimation of the reward function into a model-free reinforcement learning (RL) algorithm, resulting in a model-free PBRL algorithm. Our new algorithm is based on Relative Entropy Policy Search (REPS), enabling us to utilize stochastic policies and to directly control the greediness of the policy update. REPS decreases exploration of the policy slowly by limiting the relative entropy of the policy update, which ensures that the algorithm is provided with a versatile set of trajectories, and consequently with informative preferences. The preference-based estimation is computed using a sample-based Bayesian method, which can also estimate the uncertainty of the utility. Additionally, we also compare to a linear solvable approximation, based on inverse RL. We show that both approaches perform favourably to the current state-of-the-art. The overall result is an algorithm that can learn non-parametric continuous action policies from a small number of preferences.

The popular Q-learning algorithm is known to overestimate action values under certain conditions. It was not previously known whether, in practice, such overestimations are common, whether they harm performance, and whether they can generally be prevented. In this paper, we answer all these questions affirmatively. In particular, we first show that the recent DQN algorithm, which combines Q-learning with a deep neural network, suffers from substantial overestimations in some games in the Atari 2600 domain. We then show that the idea behind the Double Q-learning algorithm, which was introduced in a tabular setting, can be generalized to work with large-scale function approximation. We propose a specific adaptation to the DQN algorithm and show that the resulting algorithm not only reduces the observed overestimations, as hypothesized, but that this also leads to much better performance on several games.

Inverse Reinforcement Learning (IRL) deals with the problem of recovering the reward function optimized by an expert given a set of demonstrations of the expert's policy.Most IRL algorithms need to repeatedly compute the optimal policy for different reward functions.This paper proposes a new IRL approach that allows to recover the reward function without the need of solving any "direct" RL problem.The idea is to find the reward function that minimizes the gradient of a parameterized representation of the expert's policy.In particular, when the reward function can be represented as a linear combination of some basis functions, we will show that the aforementioned optimization problem can be efficiently solved.We present an empirical evaluation of the proposed approach on a multidimensional version of the Linear-Quadratic Regulator (LQR) both in the case where the parameters of the expert's policy are known and in the (more realistic) case where the parameters of the expert's policy need to be inferred from the expert's demonstrations.Finally, the algorithm is compared against the state-of-the-art on the mountain car domain, where the expert's policy is unknown.

We introduce a model-free algorithm for learning in Markov decision processes with parameterized actions—discrete actions with continuous parameters. At each step the agent must select both which action to use and which parameters to use with that action. We introduce the Q-PAMDP algorithm for learning in these domains, show that it converges to a local optimum, and compare it to direct policy search in the goal-scoring and Platform domains.

In many real-world reinforcement learning problems, we have access to an existing dataset and would like to use it to evaluate various learning approaches. Typically, one would prefer not to deploy a fixed policy, but rather an algorithm that learns to improve its behavior as it gains more experience. Therefore, we seek to evaluate how a proposed algorithm learns in our environment, meaning we need to evaluate how an algorithm would have gathered experience if it were run online. In this work, we develop three new evaluation approaches which guarantee that, given some history, algorithms are fed samples from the distribution that they would have encountered if they were run online. Additionally, we are the first to propose an approach that is provably unbiased given finite data, eliminating bias due to the length of the evaluation. Finally, we compare the sample-efficiency of these approaches on multiple datasets, including one from a real-world deployment of an educational game.

Computational agents often need to learn policies that involve many control variables, e.g., a robot needs to control several joints simultaneously. Learning a policy with a high number of parameters, however, usually requires a large number of training samples. We introduce a reinforcement learning method for sample-efficient policy search that exploits correlations between control variables. Such correlations are particularly frequent in motor skill learning tasks. The introduced method uses Variational Inference to estimate policy parameters, while at the same time uncovering a low-dimensional latent space of controls. Prior knowledge about the task and the structure of the learning agent can be provided by specifying groups of potentially correlated parameters. This information is then used to impose sparsity constraints on the mapping between the high-dimensional space of controls and a lower-dimensional latent space. In experiments with a simulated bi-manual manipulator, the new approach effectively identifies synergies between joints, performs efficient low-dimensional policy search, and outperforms state-of-the-art policy search methods.

We present a model-based approach to solving Markov decision processes (MDPs) in which the system dynamics are learned using conditional mean embeddings (CMEs). This class of methods comes with strong performance guarantees, and enables planning to be performed in an induced finite (pseudo-)MDP, which approximates the MDP, but can be solved exactly using dynamic programming. Two drawbacks of existing methods exist: firstly, the size of the induced finite (pseudo-)MDP scales quadratically with the amount of data used to learn the model, costing much memory and time when planning with the learned model; secondly, learning the CME itself using powerful kernel least-squares is costly – a second computational bottleneck. We present an algorithm which maintains a rich kernelized CME model class, but solves both problems: firstly we demonstrate that the loss function for the CME model suggests a principled approach to compressing the induced (pseudo-)MDP, leading to faster planning, while maintaining guarantees; secondly we propose to learn the CME model itself using fast sparse-greedy kernel regression well-suited to the RL context. We demonstrate superior performance to existing methods in this class of modelbased approaches on a range of MDPs.

Within the framework of probably approximately correct Markov decision processes (PAC-MDP), much theoretical work has focused on methods to attain near optimality after a relatively long period of learning and exploration. However, practical concerns require the attainment of satisfactory behavior within a short period of time. In this paper, we relax the PAC-MDP conditions to reconcile theoretically driven exploration methods and practical needs. We propose simple algorithms for discrete and continuous state spaces, and illustrate the benefits of our proposed relaxation via theoretical analyses and numerical examples. Our algorithms also maintain anytime error bounds and average loss bounds. Our approach accommodates both Bayesian and non-Bayesian methods.

We consider the off-policy evaluation problem in Markov decision processes with function approximation. We propose a generalization of the recently introduced emphatic temporal differences (ETD) algorithm, which encompasses the original ETD(λ), as well as several other off-policy evaluation algorithms as special cases. We call this framework ETD(λ, β), where our introduced parameter β controls the decay rate of an importance-sampling term. We study conditions under which the projected fixed-point equation underlying ETD(λ, β) involves a contraction operator, allowing us to present the first asymptotic error bounds (bias) for ETD(λ, β). Our results show that the original ETD algorithm always involves a contraction operator, and its bias is bounded. Moreover, by controlling β, our proposed generalization allows trading-off bias for variance reduction, thereby achieving a lower total error.

This paper introduces new optimality-preserving operators on Q-functions. We first describe an operator for tabular representations, the consistent Bellman operator, which incorporates a notion of local policy consistency. We show that this local consistency leads to an increase in the action gap at each state; increasing this gap, we argue, mitigates the undesirable effects of approximation and estimation errors on the induced greedy policies. This operator can also be applied to discretized continuous space and time problems, and we provide empirical results evidencing superior performance in this context. Extending the idea of a locally consistent operator, we then derive sufficient conditions for an operator to preserve optimality, leading to a family of operators which includes our consistent Bellman operator. As corollaries we provide a proof of optimality for Baird's advantage learning algorithm and derive other gap-increasing operators with interesting properties. We conclude with an empirical study on 60 Atari 2600 games illustrating the strong potential of these new operators.