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Jan Peters (Project leader)
Research Group Leader
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Philipp Hennig
Max Planck Research Group Leader
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Jens Kober
Alumni
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11 results

2012


PAC-Bayesian Inequalities for Martingales

Seldin, Y., Laviolette, F., Cesa-Bianchi, N., Shawe-Taylor, J., Auer, P.

IEEE Transactions on Information Theory, 58(12):7086-7093, June 2012 (article)

Abstract
We present a set of high-probability inequalities that control the concentration of weighted averages of multiple (possibly uncountably many) simultaneously evolving and interdependent martingales. We also present a comparison inequality that bounds expectation of a convex function of martingale difference type variables by expectation of the same function of independent Bernoulli variables. This inequality is applied to derive a tighter analog of Hoeffding-Azuma inequality.

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2012

PDF Web DOI Project Page [BibTex]


Structured Apprenticeship Learning

Boularias, A., Kroemer, O., Peters, J.

In European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), 2012 (inproceedings)

PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]


Hierarchical Relative Entropy Policy Search

Daniel, C., Neumann, G., Peters, J.

In Fifteenth International Conference on Artificial Intelligence and Statistics, 22, pages: 273-281, JMLR Proceedings, (Editors: Lawrence, N. D. and Girolami, M.), JMLR.org, AISTATS, April 2012 (inproceedings)

Abstract
Many real-world problems are inherently hierarchically structured. The use of this structure in an agent's policy may well be the key to improved scalability and higher performance. However, such hierarchical structures cannot be exploited by current policy search algorithms. We will concentrate on a basic, but highly relevant hierarchy - the `mixed option' policy. Here, a gating network fi rst decides which of the options to execute and, subsequently, the option-policy determines the action. In this paper, we reformulate learning a hierarchical policy as a latent variable estimation problem and subsequently extend the Relative Entropy Policy Search (REPS) to the latent variable case. We show that our Hierarchical REPS can learn versatile solutions while also showing an increased performance in terms of learning speed and quality of the found policy in comparison to the nonhierarchical approach.

PDF Web Project Page [BibTex]

PDF Web Project Page [BibTex]

2011


Policy Search for Motor Primitives in Robotics

Kober, J., Peters, J.

Machine Learning, 84(1-2):171-203, July 2011 (article)

Abstract
Many motor skills in humanoid robotics can be learned using parametrized motor primitives. While successful applications to date have been achieved with imitation learning, most of the interesting motor learning problems are high-dimensional reinforcement learning problems. These problems are often beyond the reach of current reinforcement learning methods. In this paper, we study parametrized policy search methods and apply these to benchmark problems of motor primitive learning in robotics. We show that many well-known parametrized policy search methods can be derived from a general, common framework. This framework yields both policy gradient methods and expectation-maximization (EM) inspired algorithms. We introduce a novel EM-inspired algorithm for policy learning that is particularly well-suited for dynamical system motor primitives. We compare this algorithm, both in simulation and on a real robot, to several well-known parametrized policy search methods such as episodic REINFORCE, ‘Vanilla’ Policy Gradients with optimal baselines, episodic Natural Actor Critic, and episodic Reward-Weighted Regression. We show that the proposed method out-performs them on an empirical benchmark of learning dynamical system motor primitives both in simulation and on a real robot. We apply it in the context of motor learning and show that it can learn a complex Ball-in-a-Cup task on a real Barrett WAM™ robot arm.

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Relative Entropy Inverse Reinforcement Learning

Boularias, A., Kober, J., Peters, J.

In JMLR Workshop and Conference Proceedings Volume 15: AISTATS 2011, pages: 182-189, (Editors: Gordon, G. , D. Dunson, M. Dudík ), MIT Press, Cambridge, MA, USA, Fourteenth International Conference on Artificial Intelligence and Statistics, April 2011 (inproceedings)

Abstract
We consider the problem of imitation learning where the examples, demonstrated by an expert, cover only a small part of a large state space. Inverse Reinforcement Learning (IRL) provides an efficient tool for generalizing the demonstration, based on the assumption that the expert is optimally acting in a Markov Decision Process (MDP). Most of the past work on IRL requires that a (near)-optimal policy can be computed for different reward functions. However, this requirement can hardly be satisfied in systems with a large, or continuous, state space. In this paper, we propose a model-free IRL algorithm, where the relative entropy between the empirical distribution of the state-action trajectories under a uniform policy and their distribution under the learned policy is minimized by stochastic gradient descent. We compare this new approach to well-known IRL algorithms using approximate MDP models. Empirical results on simulated car racing, gridworld and ball-in-a-cup problems show that our approach is able to learn good policies from a small number of demonstrations.

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PDF Web Project Page [BibTex]


PILCO: A Model-Based and Data-Efficient Approach to Policy Search

Deisenroth, MP. Rasmussen, CE.

In Proceedings of the 28th International Conference on Machine Learning, ICML 2011, pages: 465-472, (Editors: L Getoor and T Scheffer), Omnipress, 2011 (inproceedings)

Abstract
In this paper, we introduce PILCO, a practical, data-efficient model-based policy search method. PILCO reduces model bias, one of the key problems of model-based reinforcement learning, in a principled way. By learning a probabilistic dynamics model and explicitly incorporating model uncertainty into long-term planning, PILCO can cope with very little data and facilitates learning from scratch in only a few trials. Policy evaluation is performed in closed form using state-of-the-art approximate inference. Furthermore, policy gradients are computed analytically for policy improvement. We report unprecedented learning efficiency on challenging and high-dimensional control tasks.

Web Project Page [BibTex]

Web Project Page [BibTex]


Optimal Reinforcement Learning for Gaussian Systems

Hennig, P.

In Advances in Neural Information Processing Systems 24, pages: 325-333, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

Abstract
The exploration-exploitation trade-off is among the central challenges of reinforcement learning. The optimal Bayesian solution is intractable in general. This paper studies to what extent analytic statements about optimal learning are possible if all beliefs are Gaussian processes. A first order approximation of learning of both loss and dynamics, for nonlinear, time-varying systems in continuous time and space, subject to a relatively weak restriction on the dynamics, is described by an infinite-dimensional partial differential equation. An approximate finitedimensional projection gives an impression for how this result may be helpful.

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PDF Web Project Page Project Page [BibTex]


A Non-Parametric Approach to Dynamic Programming

Kroemer, O., Peters, J.

In Advances in Neural Information Processing Systems 24, pages: 1719-1727, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

Abstract
In this paper, we consider the problem of policy evaluation for continuousstate systems. We present a non-parametric approach to policy evaluation, which uses kernel density estimation to represent the system. The true form of the value function for this model can be determined, and can be computed using Galerkin’s method. Furthermore, we also present a unified view of several well-known policy evaluation methods. In particular, we show that the same Galerkin method can be used to derive Least-Squares Temporal Difference learning, Kernelized Temporal Difference learning, and a discrete-state Dynamic Programming solution, as well as our proposed method. In a numerical evaluation of these algorithms, the proposed approach performed better than the other methods.

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PDF Web Project Page [BibTex]


PAC-Bayesian Analysis of Contextual Bandits

Seldin, Y., Auer, P., Laviolette, F., Shawe-Taylor, J., Ortner, R.

In Advances in Neural Information Processing Systems 24, pages: 1683-1691, (Editors: J Shawe-Taylor and RS Zemel and P Bartlett and F Pereira and KQ Weinberger), Twenty-Fifth Annual Conference on Neural Information Processing Systems (NIPS), 2011 (inproceedings)

Abstract
We derive an instantaneous (per-round) data-dependent regret bound for stochastic multiarmed bandits with side information (also known as contextual bandits). The scaling of our regret bound with the number of states (contexts) $N$ goes as $\sqrt{N I_{\rho_t}(S;A)}$, where $I_{\rho_t}(S;A)$ is the mutual information between states and actions (the side information) used by the algorithm at round $t$. If the algorithm uses all the side information, the regret bound scales as $\sqrt{N \ln K}$, where $K$ is the number of actions (arms). However, if the side information $I_{\rho_t}(S;A)$ is not fully used, the regret bound is significantly tighter. In the extreme case, when $I_{\rho_t}(S;A) = 0$, the dependence on the number of states reduces from linear to logarithmic. Our analysis allows to provide the algorithm large amount of side information, let the algorithm to decide which side information is relevant for the task, and penalize the algorithm only for the side information that it is using de facto. We also present an algorithm for multiarmed bandits with side information with computational complexity that is a linear in the number of actions.

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PDF PDF Web Project Page [BibTex]

2010


Relative Entropy Policy Search

Peters, J., Mülling, K., Altun, Y.

In Proceedings of the Twenty-Fourth National Conference on Artificial Intelligence, pages: 1607-1612, (Editors: Fox, M. , D. Poole), AAAI Press, Menlo Park, CA, USA, Twenty-Fourth National Conference on Artificial Intelligence (AAAI-10), July 2010 (inproceedings)

Abstract
Policy search is a successful approach to reinforcement learning. However, policy improvements often result in the loss of information. Hence, it has been marred by premature convergence and implausible solutions. As first suggested in the context of covariant policy gradients (Bagnell and Schneider 2003), many of these problems may be addressed by constraining the information loss. In this paper, we continue this path of reasoning and suggest the Relative Entropy Policy Search (REPS) method. The resulting method differs significantly from previous policy gradient approaches and yields an exact update step. It works well on typical reinforcement learning benchmark problems.

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2010

PDF Web Project Page [BibTex]

2009


Gaussian Process Dynamic Programming

Deisenroth, M., Rasmussen, C., Peters, J.

Neurocomputing, 72(7-9):1508-1524, March 2009 (article)

Abstract
Reinforcement learning (RL) and optimal control of systems with contin- uous states and actions require approximation techniques in most interesting cases. In this article, we introduce Gaussian process dynamic programming (GPDP), an approximate value-function based RL algorithm. We consider both a classic optimal control problem, where problem-specific prior knowl- edge is available, and a classic RL problem, where only very general priors can be used. For the classic optimal control problem, GPDP models the unknown value functions with Gaussian processes and generalizes dynamic programming to continuous-valued states and actions. For the RL problem, GPDP starts from a given initial state and explores the state space using Bayesian active learning. To design a fast learner, available data has to be used efficiently. Hence, we propose to learn probabilistic models of the a priori unknown transition dynamics and the value functions on the fly. In both cases, we successfully apply the resulting continuous-valued controllers to the under-actuated pendulum swing up and analyze the performances of the suggested algorithms. It turns out that GPDP uses data very efficiently and can be applied to problems, where classic dynamic programming would be cumbersome.

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2009

PDF PDF DOI Project Page [BibTex]