55,730 research outputs found
Online algorithms for POMDPs with continuous state, action, and observation spaces
Online solvers for partially observable Markov decision processes have been
applied to problems with large discrete state spaces, but continuous state,
action, and observation spaces remain a challenge. This paper begins by
investigating double progressive widening (DPW) as a solution to this
challenge. However, we prove that this modification alone is not sufficient
because the belief representations in the search tree collapse to a single
particle causing the algorithm to converge to a policy that is suboptimal
regardless of the computation time. This paper proposes and evaluates two new
algorithms, POMCPOW and PFT-DPW, that overcome this deficiency by using
weighted particle filtering. Simulation results show that these modifications
allow the algorithms to be successful where previous approaches fail.Comment: Added Multilane sectio
Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution
We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case
Risk-sensitive Inverse Reinforcement Learning via Semi- and Non-Parametric Methods
The literature on Inverse Reinforcement Learning (IRL) typically assumes that
humans take actions in order to minimize the expected value of a cost function,
i.e., that humans are risk neutral. Yet, in practice, humans are often far from
being risk neutral. To fill this gap, the objective of this paper is to devise
a framework for risk-sensitive IRL in order to explicitly account for a human's
risk sensitivity. To this end, we propose a flexible class of models based on
coherent risk measures, which allow us to capture an entire spectrum of risk
preferences from risk-neutral to worst-case. We propose efficient
non-parametric algorithms based on linear programming and semi-parametric
algorithms based on maximum likelihood for inferring a human's underlying risk
measure and cost function for a rich class of static and dynamic
decision-making settings. The resulting approach is demonstrated on a simulated
driving game with ten human participants. Our method is able to infer and mimic
a wide range of qualitatively different driving styles from highly risk-averse
to risk-neutral in a data-efficient manner. Moreover, comparisons of the
Risk-Sensitive (RS) IRL approach with a risk-neutral model show that the RS-IRL
framework more accurately captures observed participant behavior both
qualitatively and quantitatively, especially in scenarios where catastrophic
outcomes such as collisions can occur.Comment: Submitted to International Journal of Robotics Research; Revision 1:
(i) Clarified minor technical points; (ii) Revised proof for Theorem 3 to
hold under weaker assumptions; (iii) Added additional figures and expanded
discussions to improve readabilit
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