41,380 research outputs found
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
Algorithmic aspects of 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.National Science Foundation (U.S.) (CMMI-0856063
Risk-Sensitive Reinforcement Learning: A Constrained Optimization Viewpoint
The classic objective in a reinforcement learning (RL) problem is to find a
policy that minimizes, in expectation, a long-run objective such as the
infinite-horizon discounted or long-run average cost. In many practical
applications, optimizing the expected value alone is not sufficient, and it may
be necessary to include a risk measure in the optimization process, either as
the objective or as a constraint. Various risk measures have been proposed in
the literature, e.g., mean-variance tradeoff, exponential utility, the
percentile performance, value at risk, conditional value at risk, prospect
theory and its later enhancement, cumulative prospect theory. In this article,
we focus on the combination of risk criteria and reinforcement learning in a
constrained optimization framework, i.e., a setting where the goal to find a
policy that optimizes the usual objective of infinite-horizon
discounted/average cost, while ensuring that an explicit risk constraint is
satisfied. We introduce the risk-constrained RL framework, cover popular risk
measures based on variance, conditional value-at-risk and cumulative prospect
theory, and present a template for a risk-sensitive RL algorithm. We survey
some of our recent work on this topic, covering problems encompassing
discounted cost, average cost, and stochastic shortest path settings, together
with the aforementioned risk measures in a constrained framework. This
non-exhaustive survey is aimed at giving a flavor of the challenges involved in
solving a risk-sensitive RL problem, and outlining some potential future
research directions
State-Augmentation Transformations for Risk-Sensitive Reinforcement Learning
In the framework of MDP, although the general reward function takes three
arguments-current state, action, and successor state; it is often simplified to
a function of two arguments-current state and action. The former is called a
transition-based reward function, whereas the latter is called a state-based
reward function. When the objective involves the expected cumulative reward
only, this simplification works perfectly. However, when the objective is
risk-sensitive, this simplification leads to an incorrect value. We present
state-augmentation transformations (SATs), which preserve the reward sequences
as well as the reward distributions and the optimal policy in risk-sensitive
reinforcement learning. In risk-sensitive scenarios, firstly we prove that, for
every MDP with a stochastic transition-based reward function, there exists an
MDP with a deterministic state-based reward function, such that for any given
(randomized) policy for the first MDP, there exists a corresponding policy for
the second MDP, such that both Markov reward processes share the same reward
sequence. Secondly we illustrate that two situations require the proposed SATs
in an inventory control problem. One could be using Q-learning (or other
learning methods) on MDPs with transition-based reward functions, and the other
could be using methods, which are for the Markov processes with a deterministic
state-based reward functions, on the Markov processes with general reward
functions. We show the advantage of the SATs by considering Value-at-Risk as an
example, which is a risk measure on the reward distribution instead of the
measures (such as mean and variance) of the distribution. We illustrate the
error in the reward distribution estimation from the direct use of Q-learning,
and show how the SATs enable a variance formula to work on Markov processes
with general reward functions
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