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Value function approximation in reinforcement learning using the Fourier basis
, 2008
"... We describe the Fourier Basis, a linear value function approximation scheme based on the Fourier Series. We empirically evaluate its properties, and demonstrate that it performs well compared to Radial Basis Functions and the Polynomial Basis, the two most popular fixed bases for linear value functi ..."
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Cited by 45 (14 self)
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We describe the Fourier Basis, a linear value function approximation scheme based on the Fourier Series. We empirically evaluate its properties, and demonstrate that it performs well compared to Radial Basis Functions and the Polynomial Basis, the two most popular fixed bases for linear value function approximation, and is competitive with learned ProtoValue Functions even though no extra experience or computation is required. 1
Reinforcement Learning in Robotics: A Survey
"... Reinforcement learning offers to robotics a framework and set oftoolsfor the design of sophisticated and hardtoengineer behaviors. Conversely, the challenges of robotic problems provide both inspiration, impact, and validation for developments in reinforcement learning. The relationship between di ..."
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Cited by 39 (2 self)
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Reinforcement learning offers to robotics a framework and set oftoolsfor the design of sophisticated and hardtoengineer behaviors. Conversely, the challenges of robotic problems provide both inspiration, impact, and validation for developments in reinforcement learning. The relationship between disciplines has sufficient promise to be likened to that between physics and mathematics. In this article, we attempt to strengthen the links between the two research communities by providing a survey of work in reinforcement learning for behavior generation in robots. We highlight both key challenges in robot reinforcement learning as well as notable successes. We discuss how contributions tamed the complexity of the domain and study the role of algorithms, representations, and prior knowledge in achieving these successes. As a result, a particular focus of our paper lies on the choice between modelbased and modelfree as well as between value functionbased and policy search methods. By analyzing a simple problem in some detail we demonstrate how reinforcement learning approaches may be profitably applied, and
Robot Learning from Demonstration by Constructing Skill Trees
"... We describe CST, an online algorithm for constructing skill trees from demonstration trajectories. CST segments a demonstration trajectory into a chain of component skills, where each skill has a goal and is assigned a suitable abstraction from an abstraction library. These properties permit skills ..."
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Cited by 34 (5 self)
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We describe CST, an online algorithm for constructing skill trees from demonstration trajectories. CST segments a demonstration trajectory into a chain of component skills, where each skill has a goal and is assigned a suitable abstraction from an abstraction library. These properties permit skills to be improved efficiently using a policy learning algorithm. Chains from multiple demonstration trajectories are merged into a skill tree. We show that CST can be used to acquire skills from human demonstration in a dynamic continuous domain, and from both expert demonstration and learned control sequences on the uBot5 mobile manipulator. 1 1
Feature Selection Using Regularization in Approximate Linear Programs for Markov Decision Processes
"... Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. ..."
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Cited by 29 (11 self)
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Approximate dynamic programming has been used successfully in a large variety of domains, but it relies on a small set of provided approximation features to calculate solutions reliably. Large and rich sets of features can cause existing algorithms to overfit because of a limited number of samples. We address this shortcoming using L1 regularization in approximate linear programming. Because the proposed method can automatically select the appropriate richness of features, its performance does not degrade with an increasing number of features. These results rely on new and stronger sampling bounds for regularized approximate linear programs. We also propose a computationally efficient homotopy method. The empirical evaluation of the approach shows that the proposed method performs well on simple MDPs and standard benchmark problems. 1.
Kalman Temporal Differences
 Journal of Artificial Intelligence Research (JAIR
, 2010
"... Because reinforcement learning suffers from a lack of scalability, online value (and Q) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the foll ..."
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Cited by 25 (18 self)
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Because reinforcement learning suffers from a lack of scalability, online value (and Q) function approximation has received increasing interest this last decade. This contribution introduces a novel approximation scheme, namely the Kalman Temporal Differences (KTD) framework, that exhibits the following features: sampleefficiency, nonlinear approximation, nonstationarity handling and uncertainty management. A first KTDbased algorithm is provided for deterministic Markov Decision Processes (MDP) which produces biased estimates in the case of stochastic transitions. Than the eXtended KTD framework (XKTD), solving stochastic MDP, is described. Convergence is analyzed for special cases for both deterministic and stochastic transitions. Related algorithms are experimented on classical benchmarks. They compare favorably to the state of the art while exhibiting the announced features. 1.
A unifying framework for computational reinforcement learning theory
, 2009
"... Computational learning theory studies mathematical models that allow one to formally analyze and compare the performance of supervisedlearning algorithms such as their sample complexity. While existing models such as PAC (Probably Approximately Correct) have played an influential role in understand ..."
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Cited by 23 (7 self)
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Computational learning theory studies mathematical models that allow one to formally analyze and compare the performance of supervisedlearning algorithms such as their sample complexity. While existing models such as PAC (Probably Approximately Correct) have played an influential role in understanding the nature of supervised learning, they have not been as successful in reinforcement learning (RL). Here, the fundamental barrier is the need for active exploration in sequential decision problems. An RL agent tries to maximize longterm utility by exploiting its knowledge about the problem, but this knowledge has to be acquired by the agent itself through exploring the problem that may reduce shortterm utility. The need for active exploration is common in many problems in daily life, engineering, and sciences. For example, a Backgammon program strives to take good moves to maximize the probability of winning a game, but sometimes it may try novel and possibly harmful moves to discover how the opponent reacts in the hope of discovering a better gameplaying strategy. It has been known since the early days of RL that a good tradeoff between exploration and exploitation is critical for the agent to learn fast (i.e., to reach nearoptimal strategies
Linear Complementarity for Regularized Policy Evaluation and Improvement
, 2010
"... Recent work in reinforcement learning has emphasized the power of L1 regularization to perform feature selection and prevent overfitting. We propose formulating the L1 regularized linear fixed point problem as a linear complementarity problem (LCP). This formulation offers several advantages over th ..."
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Cited by 23 (4 self)
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Recent work in reinforcement learning has emphasized the power of L1 regularization to perform feature selection and prevent overfitting. We propose formulating the L1 regularized linear fixed point problem as a linear complementarity problem (LCP). This formulation offers several advantages over the LARSinspired formulation, LARSTD. The LCP formulation allows the use of efficient offtheshelf solvers, leads to a new uniqueness result, and can be initialized with starting points from similar problems (warm starts). We demonstrate that warm starts, as well as the efficiency of LCP solvers, can speed up policy iteration. Moreover, warm starts permit a form of modified policy iteration that can be used to approximate a “greedy” homotopy path, a generalization of the LARSTD homotopy path that combines policy evaluation and optimization.
LSTD with random projections
 In Advances in Neural Information Processing Systems
, 2010
"... We consider the problem of reinforcement learning in highdimensional spaces when the number of features is bigger than the number of samples. In particular, we study the leastsquares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection f ..."
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Cited by 17 (5 self)
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We consider the problem of reinforcement learning in highdimensional spaces when the number of features is bigger than the number of samples. In particular, we study the leastsquares temporal difference (LSTD) learning algorithm when a space of low dimension is generated with a random projection from a highdimensional space. We provide a thorough theoretical analysis of the LSTD with random projections and derive performance bounds for the resulting algorithm. We also show how the error of LSTD with random projections is propagated through the iterations of a policy iteration algorithm and provide a performance bound for the resulting leastsquares policy iteration (LSPI) algorithm. 1
Predictive state temporal difference learning
"... We propose a new approach to value function approximation which combines linear temporal difference reinforcement learning with subspace identification. In practical applications, reinforcement learning (RL) is complicated by the fact that state is either highdimensional or partially observable. Th ..."
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Cited by 17 (7 self)
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We propose a new approach to value function approximation which combines linear temporal difference reinforcement learning with subspace identification. In practical applications, reinforcement learning (RL) is complicated by the fact that state is either highdimensional or partially observable. Therefore, RL methods are designed to work with features of state rather than state itself, and the success or failure of learning is often determined by the suitability of the selected features. By comparison, subspace identification (SSID) methods are designed to select a feature set which preserves as much information as possible about state. In this paper we connect the two approaches, looking at the problem of reinforcement learning with a large set of features, each of which may only be marginally useful for value function approximation. We introduce a new algorithm for this situation, called Predictive State Temporal Difference (PSTD) learning. As in SSID for predictive state representations, PSTD finds a linear compression operator that projects a large set of features down to a small set that preserves the maximum amount of predictive information. As in RL, PSTD then uses a Bellman recursion to estimate a value function. We discuss the connection between PSTD and prior approaches in RL and SSID. We prove that PSTD is statistically consistent, perform several experiments that illustrate its properties, and demonstrate its potential on a difficult optimal stopping problem. 1