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We consider the problem of learning the optimal action-value function in the discounted-reward Markov decision processes (MDPs). We prove a new PAC bound on the sample-complexity of model-based value iteration algorithm in the presence of the generative model, which indicates that for an MDP with N state-action pairs and the discount factor γ ∈ [0, 1) only… (More)

In this paper, we propose a novel policy iteration method, called dynamic policy programming (DPP), to estimate the optimal policy in the infinite-horizon Markov decision processes. DPP is an incremental algorithm that forces a gradual change in policy update. This allows us to prove finite-iteration and asymptotic ℓ ∞-norm performance-loss bounds in the… (More)

In some reinforcement learning problems an agent may be provided with a set of input policies, perhaps learned from prior experience or provided by advisors. We present a reinforcement learning with policy advice (RLPA) algorithm which leverages this input set and learns to use the best policy in the set for the reinforcement learning task at hand. We prove… (More)

In this paper we consider the problem of online stochastic optimization of a locally smooth function under bandit feedback. We introduce the high-confidence tree (HCT) algorithm, a novel anytime X-armed bandit algorithm, and derive regret bounds matching the performance of existing state-of-the-art in terms of dependency on number of steps and smoothness… (More)

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt età la diffusion… (More)

We introduce a new convergent variant of Q-learning, called speedy Q-learning, in order to address the problem of slow convergence in the standard form of the Q-learning algorithm. We prove a PAC bound on the performance of SQL, which shows that only T = O log(1/δ)ǫ −2 (1 − γ) −4 steps are required for the SQL algorithm to converge to an ǫ-optimal… (More)

In this paper, we consider the problem of planning in the infinite-horizon discounted-reward Markov decision problems. We propose a novel iterative method, called dynamic policy programming (DPP), which updates the parametrized policy by a Bellman-like iteration. For discrete state-action case, we establish sup-norm loss bounds for the performance of the… (More)

We consider the problems of learning the optimal action-value function and the optimal policy in discounted-reward Markov decision processes (MDPs). We prove new PAC bounds on the sample-complexity of two well-known model-based reinforcement learning (RL) algorithms in the presence of a generative model of the MDP: value iteration and policy iteration. The… (More)

Finding efficient and provable methods to solve non-convex optimization problems is an outstanding challenge in machine learning and optimization theory. A popular approach used to tackle non-convex problems is to use convex relaxation techniques to find a convex surrogate for the problem. Unfortunately, convex relax-ations typically must be found on a… (More)