55 research outputs found
MDP Optimal Control under Temporal Logic Constraints
In this paper, we develop a method to automatically generate a control policy
for a dynamical system modeled as a Markov Decision Process (MDP). The control
specification is given as a Linear Temporal Logic (LTL) formula over a set of
propositions defined on the states of the MDP. We synthesize a control policy
such that the MDP satisfies the given specification almost surely, if such a
policy exists. In addition, we designate an "optimizing proposition" to be
repeatedly satisfied, and we formulate a novel optimization criterion in terms
of minimizing the expected cost in between satisfactions of this proposition.
We propose a sufficient condition for a policy to be optimal, and develop a
dynamic programming algorithm that synthesizes a policy that is optimal under
some conditions, and sub-optimal otherwise. This problem is motivated by
robotic applications requiring persistent tasks, such as environmental
monitoring or data gathering, to be performed.Comment: Technical report accompanying the CDC2011 submissio
Regret Bounds for Reinforcement Learning with Policy Advice
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 that RLPA has a
sub-linear regret of \tilde O(\sqrt{T}) relative to the best input policy, and
that both this regret and its computational complexity are independent of the
size of the state and action space. Our empirical simulations support our
theoretical analysis. This suggests RLPA may offer significant advantages in
large domains where some prior good policies are provided
Efficient Strategy Iteration for Mean Payoff in Markov Decision Processes
Markov decision processes (MDPs) are standard models for probabilistic
systems with non-deterministic behaviours. Mean payoff (or long-run average
reward) provides a mathematically elegant formalism to express performance
related properties. Strategy iteration is one of the solution techniques
applicable in this context. While in many other contexts it is the technique of
choice due to advantages over e.g. value iteration, such as precision or
possibility of domain-knowledge-aware initialization, it is rarely used for
MDPs, since there it scales worse than value iteration. We provide several
techniques that speed up strategy iteration by orders of magnitude for many
MDPs, eliminating the performance disadvantage while preserving all its
advantages
Approximate Receding Horizon Approach for Markov Decision Processes: Average Reward Case
Building on the receding horizon approach by Hernandez-Lerma andLasserre in solving Markov decision processes (MDPs),this paper first analyzes the performance of the (approximate) receding horizon approach in terms of infinite horizon average reward. In this approach, we fix a finite horizon and at each decision time, we solve the given MDP with the finite horizon for an approximately optimal current action and take the action to control the MDP.We then analyze recently proposed on-line policy improvementscheme, "roll-out," by Bertsekas and Castanon, and a generalization of the rollout algorithm, "parallel rollout" by Chang et al., in terms of the infinite horizon average reward in the framework of the (approximate) receding horizon control.We finally discuss practical implementations of these schemes via simulation
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