20,226 research outputs found
Algorithms and Conditional Lower Bounds for Planning Problems
We consider planning problems for graphs, Markov decision processes (MDPs),
and games on graphs. While graphs represent the most basic planning model, MDPs
represent interaction with nature and games on graphs represent interaction
with an adversarial environment. We consider two planning problems where there
are k different target sets, and the problems are as follows: (a) the coverage
problem asks whether there is a plan for each individual target set, and (b)
the sequential target reachability problem asks whether the targets can be
reached in sequence. For the coverage problem, we present a linear-time
algorithm for graphs and quadratic conditional lower bound for MDPs and games
on graphs. For the sequential target problem, we present a linear-time
algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic
conditional lower bound for games on graphs. Our results with conditional lower
bounds establish (i) model-separation results showing that for the coverage
problem MDPs and games on graphs are harder than graphs and for the sequential
reachability problem games on graphs are harder than MDPs and graphs; (ii)
objective-separation results showing that for MDPs the coverage problem is
harder than the sequential target problem.Comment: Accepted at ICAPS'1
Computational Approaches for Stochastic Shortest Path on Succinct MDPs
We consider the stochastic shortest path (SSP) problem for succinct Markov
decision processes (MDPs), where the MDP consists of a set of variables, and a
set of nondeterministic rules that update the variables. First, we show that
several examples from the AI literature can be modeled as succinct MDPs. Then
we present computational approaches for upper and lower bounds for the SSP
problem: (a)~for computing upper bounds, our method is polynomial-time in the
implicit description of the MDP; (b)~for lower bounds, we present a
polynomial-time (in the size of the implicit description) reduction to
quadratic programming. Our approach is applicable even to infinite-state MDPs.
Finally, we present experimental results to demonstrate the effectiveness of
our approach on several classical examples from the AI literature
Sampling-Based Methods for Factored Task and Motion Planning
This paper presents a general-purpose formulation of a large class of
discrete-time planning problems, with hybrid state and control-spaces, as
factored transition systems. Factoring allows state transitions to be described
as the intersection of several constraints each affecting a subset of the state
and control variables. Robotic manipulation problems with many movable objects
involve constraints that only affect several variables at a time and therefore
exhibit large amounts of factoring. We develop a theoretical framework for
solving factored transition systems with sampling-based algorithms. The
framework characterizes conditions on the submanifold in which solutions lie,
leading to a characterization of robust feasibility that incorporates
dimensionality-reducing constraints. It then connects those conditions to
corresponding conditional samplers that can be composed to produce values on
this submanifold. We present two domain-independent, probabilistically complete
planning algorithms that take, as input, a set of conditional samplers. We
demonstrate the empirical efficiency of these algorithms on a set of
challenging task and motion planning problems involving picking, placing, and
pushing
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