2,453 research outputs found
From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming
We consider linear programming (LP) problems in infinite dimensional spaces
that are in general computationally intractable. Under suitable assumptions, we
develop an approximation bridge from the infinite-dimensional LP to tractable
finite convex programs in which the performance of the approximation is
quantified explicitly. To this end, we adopt the recent developments in two
areas of randomized optimization and first order methods, leading to a priori
as well as a posterior performance guarantees. We illustrate the generality and
implications of our theoretical results in the special case of the long-run
average cost and discounted cost optimal control problems for Markov decision
processes on Borel spaces. The applicability of the theoretical results is
demonstrated through a constrained linear quadratic optimal control problem and
a fisheries management problem.Comment: 30 pages, 5 figure
Mean-Variance Optimization in Markov Decision Processes
We consider finite horizon Markov decision processes under performance
measures that involve both the mean and the variance of the cumulative reward.
We show that either randomized or history-based policies can improve
performance. We prove that the complexity of computing a policy that maximizes
the mean reward under a variance constraint is NP-hard for some cases, and
strongly NP-hard for others. We finally offer pseudopolynomial exact and
approximation algorithms.Comment: A full version of an ICML 2011 pape
Risk Aversion in Finite Markov Decision Processes Using Total Cost Criteria and Average Value at Risk
In this paper we present an algorithm to compute risk averse policies in
Markov Decision Processes (MDP) when the total cost criterion is used together
with the average value at risk (AVaR) metric. Risk averse policies are needed
when large deviations from the expected behavior may have detrimental effects,
and conventional MDP algorithms usually ignore this aspect. We provide
conditions for the structure of the underlying MDP ensuring that approximations
for the exact problem can be derived and solved efficiently. Our findings are
novel inasmuch as average value at risk has not previously been considered in
association with the total cost criterion. Our method is demonstrated in a
rapid deployment scenario, whereby a robot is tasked with the objective of
reaching a target location within a temporal deadline where increased speed is
associated with increased probability of failure. We demonstrate that the
proposed algorithm not only produces a risk averse policy reducing the
probability of exceeding the expected temporal deadline, but also provides the
statistical distribution of costs, thus offering a valuable analysis tool
Certified Reinforcement Learning with Logic Guidance
This paper proposes the first model-free Reinforcement Learning (RL)
framework to synthesise policies for unknown, and continuous-state Markov
Decision Processes (MDPs), such that a given linear temporal property is
satisfied. We convert the given property into a Limit Deterministic Buchi
Automaton (LDBA), namely a finite-state machine expressing the property.
Exploiting the structure of the LDBA, we shape a synchronous reward function
on-the-fly, so that an RL algorithm can synthesise a policy resulting in traces
that probabilistically satisfy the linear temporal property. This probability
(certificate) is also calculated in parallel with policy learning when the
state space of the MDP is finite: as such, the RL algorithm produces a policy
that is certified with respect to the property. Under the assumption of finite
state space, theoretical guarantees are provided on the convergence of the RL
algorithm to an optimal policy, maximising the above probability. We also show
that our method produces ''best available'' control policies when the logical
property cannot be satisfied. In the general case of a continuous state space,
we propose a neural network architecture for RL and we empirically show that
the algorithm finds satisfying policies, if there exist such policies. The
performance of the proposed framework is evaluated via a set of numerical
examples and benchmarks, where we observe an improvement of one order of
magnitude in the number of iterations required for the policy synthesis,
compared to existing approaches whenever available.Comment: This article draws from arXiv:1801.08099, arXiv:1809.0782
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