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• W2891364703 abstract "We consider the tasks of feature selection and policy evaluation based on linear value function approximation in reinforcement learning problems. High-dimension feature vectors and limited number of samples can easily cause over-fitting and computation expensive. To prevent this problem, ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -regularized method obtains sparse solutions and thus improves generalization performance. We propose an efficient ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -regularized recursive least squares-based online algorithm with O(n <sup xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2</sup> ) complexity per time-step, termed ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC. With the help of nested optimization decomposition, ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC solves a series of standard optimization problems and avoids minimizing mean squares projected Bellman error with ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -regularization directly. In ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC, we propose RC with iterative refinement to minimize the operator error, and we propose an alternating direction method of multipliers with proximal operator to minimize the fixed-point error. The convergence of ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC is established based on ordinary differential equation method and some extensions are also given. In empirical computations, some state-of-the-art ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -regularized methods are chosen as the baselines, and ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC are tested in both policy evaluation and learning control benchmarks. The empirical results show the effectiveness and advantages of ℓ <sub xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1</sub> -RC." @default.
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• W2891364703 date "2020-11-01" @default.
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• W2891364703 title "Sparse Proximal Reinforcement Learning via Nested Optimization" @default.
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• W2891364703 doi "https://doi.org/10.1109/tsmc.2018.2865505" @default.
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