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Register a new userDetecting Spiky Corruption in Markov Decision Processes
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Current reinforcement learning methods fail if the reward function is imperfect, i.e. if the agent observes reward different from what it actually receives. We study this problem within the formalism of Corrupt Reward Markov Decision Processes (CRMDPs). We show that if the reward corruption in a CRMDP is sufficiently spiky, the environment is solvable. We fully characterize the regret bound of a Spiky CRMDP, and introduce an algorithm that is able to detect its corrupt states. We show that this algorithm can be used to learn the optimal policy with any common reinforcement learning algorithm. Finally, we investigate our algorithm in a pair of simple gridworld environments, finding that our algorithm can detect the corrupt states and learn the optimal policy despite the corruption.
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We consider online learning for minimizing regret in unknown, episodic Markov decision processes (MDPs) with continuous states and actions. We develop variants of the UCRL and posterior sampling algorithms that employ nonparametric Gaussian process priors to generalize across the state and action spaces. When the transition and reward functions of the true MDP are members of the associated Reproducing Kernel Hilbert Spaces of functions induced by symmetric psd kernels (frequentist setting), we show that the algorithms enjoy sublinear regret bounds. The bounds are in terms of explicit structural parameters of the kernels, namely a novel generalization of the information gain metric from kernelized bandit, and highlight the influence of transition and reward function structure on the learning performance. Our results are applicable to multidimensional state and action spaces with composite kernel structures, and generalize results from the literature on kernelized bandits, and the adaptive control of parametric linear dynamical systems with quadratic costs.
We develop algorithms with low regret for learning episodic Markov decision processes based on kernel approximation techniques. The algorithms are based on both the Upper Confidence Bound (UCB) as well as Posterior or Thompson Sampling (PSRL) philosophies, and work in the general setting of continuous state and action spaces when the true unknown transition dynamics are assumed to have smoothness induced by an appropriate Reproducing Kernel Hilbert Space (RKHS).
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We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The setup naturally leads to novel theoretical results which are simply formulated due to the max-plus algebra structure. For example, when considering a fixed (non adaptive) finite basis, the computational complexity of approximating the optimal value function is not directly related to the number of states, but to notions of covering numbers of the state space. In order to break the curse of dimensionality in factored state-spaces, we consider adaptive basis that can adapt to particular problems leading to an algorithm similar to matching pursuit from signal processing. They currently come with no theoretical guarantees but work empirically well on simple deterministic MDPs derived from low-dimensional continuous control problems. We focus primarily on deterministic MDPs but note that the framework can be applied to all MDPs by considering measure-based formulations.
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