46 research outputs found
Value Iteration for Long-run Average Reward in Markov Decision Processes
Markov decision processes (MDPs) are standard models for probabilistic
systems with non-deterministic behaviours. Long-run average rewards provide a
mathematically elegant formalism for expressing long term performance. Value
iteration (VI) is one of the simplest and most efficient algorithmic approaches
to MDPs with other properties, such as reachability objectives. Unfortunately,
a naive extension of VI does not work for MDPs with long-run average rewards,
as there is no known stopping criterion. In this work our contributions are
threefold. (1) We refute a conjecture related to stopping criteria for MDPs
with long-run average rewards. (2) We present two practical algorithms for MDPs
with long-run average rewards based on VI. First, we show that a combination of
applying VI locally for each maximal end-component (MEC) and VI for
reachability objectives can provide approximation guarantees. Second, extending
the above approach with a simulation-guided on-demand variant of VI, we present
an anytime algorithm that is able to deal with very large models. (3) Finally,
we present experimental results showing that our methods significantly
outperform the standard approaches on several benchmarks
Robust Satisfaction of Temporal Logic Specifications via Reinforcement Learning
We consider the problem of steering a system with unknown, stochastic
dynamics to satisfy a rich, temporally layered task given as a signal temporal
logic formula. We represent the system as a Markov decision process in which
the states are built from a partition of the state space and the transition
probabilities are unknown. We present provably convergent reinforcement
learning algorithms to maximize the probability of satisfying a given formula
and to maximize the average expected robustness, i.e., a measure of how
strongly the formula is satisfied. We demonstrate via a pair of robot
navigation simulation case studies that reinforcement learning with robustness
maximization performs better than probability maximization in terms of both
probability of satisfaction and expected robustness.Comment: 8 pages, 4 figure
Robust satisfaction of temporal logic specifications via reinforcement learning
We consider the problem of steering a system with unknown, stochastic dynamics to satisfy a rich, temporally-layered task given as a signal temporal logic formula. We represent the system as a finite-memory Markov decision process with unknown transition probabilities and whose states are built from a partition of the state space. We present provably convergent reinforcement learning algorithms to maximize the probability of satisfying a given specification and to maximize the average expected robustness, i.e. a measure of how strongly the formula is satisfied. Robustness allows us to quantify progress towards satisfying a given specification. We demonstrate via a pair of robot navigation simulation case studies that, due to the quantification of progress towards satisfaction, reinforcement learning with robustness maximization performs better than probability maximization in terms of both probability of satisfaction and expected robustness with a low number of training examples
Should We Learn Probabilistic Models for Model Checking? A New Approach and An Empirical Study
Many automated system analysis techniques (e.g., model checking, model-based
testing) rely on first obtaining a model of the system under analysis. System
modeling is often done manually, which is often considered as a hindrance to
adopt model-based system analysis and development techniques. To overcome this
problem, researchers have proposed to automatically "learn" models based on
sample system executions and shown that the learned models can be useful
sometimes. There are however many questions to be answered. For instance, how
much shall we generalize from the observed samples and how fast would learning
converge? Or, would the analysis result based on the learned model be more
accurate than the estimation we could have obtained by sampling many system
executions within the same amount of time? In this work, we investigate
existing algorithms for learning probabilistic models for model checking,
propose an evolution-based approach for better controlling the degree of
generalization and conduct an empirical study in order to answer the questions.
One of our findings is that the effectiveness of learning may sometimes be
limited.Comment: 15 pages, plus 2 reference pages, accepted by FASE 2017 in ETAP
Probabilistic Guarantees for Safe Deep Reinforcement Learning
Deep reinforcement learning has been successfully applied to many control
tasks, but the application of such agents in safety-critical scenarios has been
limited due to safety concerns. Rigorous testing of these controllers is
challenging, particularly when they operate in probabilistic environments due
to, for example, hardware faults or noisy sensors. We propose MOSAIC, an
algorithm for measuring the safety of deep reinforcement learning agents in
stochastic settings. Our approach is based on the iterative construction of a
formal abstraction of a controller's execution in an environment, and leverages
probabilistic model checking of Markov decision processes to produce
probabilistic guarantees on safe behaviour over a finite time horizon. It
produces bounds on the probability of safe operation of the controller for
different initial configurations and identifies regions where correct behaviour
can be guaranteed. We implement and evaluate our approach on agents trained for
several benchmark control problems
The Complexity of Graph-Based Reductions for Reachability in Markov Decision Processes
We study the never-worse relation (NWR) for Markov decision processes with an
infinite-horizon reachability objective. A state q is never worse than a state
p if the maximal probability of reaching the target set of states from p is at
most the same value from q, regard- less of the probabilities labelling the
transitions. Extremal-probability states, end components, and essential states
are all special cases of the equivalence relation induced by the NWR. Using the
NWR, states in the same equivalence class can be collapsed. Then, actions
leading to sub- optimal states can be removed. We show the natural decision
problem associated to computing the NWR is coNP-complete. Finally, we ex- tend
a previously known incomplete polynomial-time iterative algorithm to
under-approximate the NWR