420 research outputs found
Good-for-MDPs Automata for Probabilistic Analysis and Reinforcement Learning
We characterize the class of nondeterministic -automata that can be
used for the analysis of finite Markov decision processes (MDPs). We call these
automata `good-for-MDPs' (GFM). We show that GFM automata are closed under
classic simulation as well as under more powerful simulation relations that
leverage properties of optimal control strategies for MDPs. This closure
enables us to exploit state-space reduction techniques, such as those based on
direct and delayed simulation, that guarantee simulation equivalence. We
demonstrate the promise of GFM automata by defining a new class of automata
with favorable properties - they are B\"uchi automata with low branching degree
obtained through a simple construction - and show that going beyond
limit-deterministic automata may significantly benefit reinforcement learning
The Complexity of POMDPs with Long-run Average Objectives
We study the problem of approximation of optimal values in
partially-observable Markov decision processes (POMDPs) with long-run average
objectives. POMDPs are a standard model for dynamic systems with probabilistic
and nondeterministic behavior in uncertain environments. In long-run average
objectives rewards are associated with every transition of the POMDP and the
payoff is the long-run average of the rewards along the executions of the
POMDP. We establish strategy complexity and computational complexity results.
Our main result shows that finite-memory strategies suffice for approximation
of optimal values, and the related decision problem is recursively enumerable
complete
POMDPs under Probabilistic Semantics
We consider partially observable Markov decision processes (POMDPs) with
limit-average payoff, where a reward value in the interval [0,1] is associated
to every transition, and the payoff of an infinite path is the long-run average
of the rewards. We consider two types of path constraints: (i) quantitative
constraint defines the set of paths where the payoff is at least a given
threshold lambda_1 in (0,1]; and (ii) qualitative constraint which is a special
case of quantitative constraint with lambda_1=1. We consider the computation of
the almost-sure winning set, where the controller needs to ensure that the path
constraint is satisfied with probability 1. Our main results for qualitative
path constraint are as follows: (i) the problem of deciding the existence of a
finite-memory controller is EXPTIME-complete; and (ii) the problem of deciding
the existence of an infinite-memory controller is undecidable. For quantitative
path constraint we show that the problem of deciding the existence of a
finite-memory controller is undecidable.Comment: Appears in Proceedings of the Twenty-Ninth Conference on Uncertainty
in Artificial Intelligence (UAI2013
Model-free reinforcement learning for stochastic parity games
This paper investigates the use of model-free reinforcement learning to compute the optimal value in two-player stochastic games with parity objectives. In this setting, two decision makers, player Min and player Max, compete on a finite game arena - a stochastic game graph with unknown but fixed probability distributions - to minimize and maximize, respectively, the probability of satisfying a parity objective. We give a reduction from stochastic parity games to a family of stochastic reachability games with a parameter ε, such that the value of a stochastic parity game equals the limit of the values of the corresponding simple stochastic games as the parameter ε tends to 0. Since this reduction does not require the knowledge of the probabilistic transition structure of the underlying game arena, model-free reinforcement learning algorithms, such as minimax Q-learning, can be used to approximate the value and mutual best-response strategies for both players in the underlying stochastic parity game. We also present a streamlined reduction from 112-player parity games to reachability games that avoids recourse to nondeterminism. Finally, we report on the experimental evaluations of both reductions
Formal Controller Synthesis for Continuous-Space MDPs via Model-Free Reinforcement Learning
A novel reinforcement learning scheme to synthesize policies for
continuous-space Markov decision processes (MDPs) is proposed. This scheme
enables one to apply model-free, off-the-shelf reinforcement learning
algorithms for finite MDPs to compute optimal strategies for the corresponding
continuous-space MDPs without explicitly constructing the finite-state
abstraction. The proposed approach is based on abstracting the system with a
finite MDP (without constructing it explicitly) with unknown transition
probabilities, synthesizing strategies over the abstract MDP, and then mapping
the results back over the concrete continuous-space MDP with approximate
optimality guarantees. The properties of interest for the system belong to a
fragment of linear temporal logic, known as syntactically co-safe linear
temporal logic (scLTL), and the synthesis requirement is to maximize the
probability of satisfaction within a given bounded time horizon. A key
contribution of the paper is to leverage the classical convergence results for
reinforcement learning on finite MDPs and provide control strategies maximizing
the probability of satisfaction over unknown, continuous-space MDPs while
providing probabilistic closeness guarantees. Automata-based reward functions
are often sparse; we present a novel potential-based reward shaping technique
to produce dense rewards to speed up learning. The effectiveness of the
proposed approach is demonstrated by applying it to three physical benchmarks
concerning the regulation of a room's temperature, control of a road traffic
cell, and of a 7-dimensional nonlinear model of a BMW 320i car.Comment: This work is accepted at the 11th ACM/IEEE Conference on
Cyber-Physical Systems (ICCPS
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