Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incremental Sampling-based Motion Planners Using Policy Iteration
  Methods   Recent progress in randomized motion planners has led to the development of a
new class of sampling-based algorithms that provide asymptotic optimality
guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals
that the so-called "rewiring" step in these algorithms can be interpreted as a
local policy iteration (PI) step (i.e., a local policy evaluation step followed
by a local policy improvement step) so that asymptotically, as the number of
samples tend to infinity, both algorithms converge to the optimal path almost
surely (with probability 1). Policy iteration, along with value iteration (VI)
are common methods for solving dynamic programming (DP) problems. Based on this
observation, recently, the RRT$^{\#}$ algorithm has been proposed, which
performs, during each iteration, Bellman updates (aka "backups") on those
vertices of the graph that have the potential of being part of the optimal path
(i.e., the "promising" vertices). The RRT$^{\#}$ algorithm thus utilizes
dynamic programming ideas and implements them incrementally on randomly
generated graphs to obtain high quality solutions. In this work, and based on
this key insight, we explore a different class of dynamic programming
algorithms for solving shortest-path problems on random graphs generated by
iterative sampling methods. These class of algorithms utilize policy iteration
instead of value iteration, and thus are better suited for massive
parallelization. Contrary to the RRT* algorithm, the policy improvement during
the rewiring step is not performed only locally but rather on a set of vertices
that are classified as "promising" during the current iteration. This tends to
speed-up the whole process. The resulting algorithm, aptly named Policy
Iteration-RRT$^{\#}$ (PI-RRT$^{\#}$) is the first of a new class of DP-inspired
algorithms for randomized motion planning that utilize PI methods.

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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: astro-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph