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Register a new userSparse tree search optimality guarantees in POMDPs with continuous observation spaces
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Added by
Zachary Sunberg
Publication date
2019
fields
Informatics Engineering
and research's language is
English
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Partially observable Markov decision processes (POMDPs) with continuous state and observation spaces have powerful flexibility for representing real-world decision and control problems but are notoriously difficult to solve. Recent online sampling-based algorithms that use observation likelihood weighting have shown unprecedented effectiveness in domains with continuous observation spaces. However there has been no formal theoretical justification for this technique. This work offers such a justification, proving that a simplified algorithm, partially observable weighted sparse sampling (POWSS), will estimate Q-values accurately with high probability and can be made to perform arbitrarily near the optimal solution by increasing computational power.
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Many processes, such as discrete event systems in engineering or population dynamics in biology, evolve in discrete space and continuous time. We consider the problem of optimal decision making in such discrete state and action space systems under partial observability. This places our work at the intersection of optimal filtering and optimal control. At the current state of research, a mathematical description for simultaneous decision making and filtering in continuous time with finite state and action spaces is still missing. In this paper, we give a mathematical description of a continuous-time partial observable Markov decision process (POMDP). By leveraging optimal filtering theory we derive a Hamilton-Jacobi-Bellman (HJB) type equation that characterizes the optimal solution. Using techniques from deep learning we approximately solve the resulting partial integro-differential equation. We present (i) an approach solving the decision problem offline by learning an approximation of the value function and (ii) an online algorithm which provides a solution in belief space using deep reinforcement learning. We show the applicability on a set of toy examples which pave the way for future methods providing solutions for high dimensional problems.
This paper presents the first ever approach for solving emph{continuous-observation} Decentralized Partially Observable Markov Decision Processes (Dec-POMDPs) and their semi-Markovian counterparts, Dec-POSMDPs. This contribution is especially important in robotics, where a vast number of sensors provide continuous observation data. A continuous-observation policy representation is introduced using Stochastic Kernel-based Finite State Automata (SK-FSAs). An SK-FSA search algorithm titled Entropy-based Policy Search using Continuous Kernel Observations (EPSCKO) is introduced and applied to the first ever continuous-observation Dec-POMDP/Dec-POSMDP domain, where it significantly outperforms state-of-the-art discrete approaches. This methodology is equally applicable to Dec-POMDPs and Dec-POSMDPs, though the empirical analysis presented focuses on Dec-POSMDPs due to their higher scalability. To improve convergence, an entropy injection policy search acceleration approach for both continuous and discrete observation cases is also developed and shown to improve convergence rates without degrading policy quality.
Partially-Observable Markov Decision Processes (POMDPs) are a well-known stochastic model for sequential decision making under limited information. We consider the EXPTIME-hard problem of synthesising policies that almost-surely reach some goal state without ever visiting a bad state. In particular, we are interested in computing the winning region, that is, the set of system configurations from which a policy exists that satisfies the reachability specification. A direct application of such a winning region is the safe exploration of POMDPs by, for instance, restricting the behavior of a reinforcement learning agent to the region. We present two algorithms: A novel SAT-based iterative approach and a decision-diagram based alternative. The empirical evaluation demonstrates the feasibility and efficacy of the approaches.
Urban traffic scenarios often require a high degree of cooperation between traffic participants to ensure safety and efficiency. Observing the behavior of others, humans infer whether or not others are cooperating. This work aims to extend the capabilities of automated vehicles, enabling them to cooperate implicitly in heterogeneous environments. Continuous actions allow for arbitrary trajectories and hence are applicable to a much wider class of problems than existing cooperative approaches with discrete action spaces. Based on cooperative modeling of other agents, Monte Carlo Tree Search (MCTS) in conjunction with Decoupled-UCT evaluates the action-values of each agent in a cooperative and decentralized way, respecting the interdependence of actions among traffic participants. The extension to continuous action spaces is addressed by incorporating novel MCTS-specific enhancements for efficient search space exploration. The proposed algorithm is evaluated under different scenarios, showing that the algorithm is able to achieve effective cooperative planning and generate solutions egocentric planning fails to identify.
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing representation learning techniques that can incorporate known physical constraints into the learned representation. As one example, in many applications that involve a signal propagating through physical media (e.g., optics, acoustics, fluid dynamics, etc), it is known that the dynamics of the signal must satisfy constraints imposed by the wave equation. Here we propose a matrix factorization technique that decomposes such signals into a sum of components, where each component is regularized to ensure that it satisfies wave equation constraints. Although our proposed formulation is non-convex, we prove that our model can be efficiently solved to global optimality in polynomial time. We demonstrate the benefits of our work by applications in structural health monitoring, where prior work has attempted to solve this problem using sparse dictionary learning approaches that do not come with any theoretical guarantees regarding convergence to global optimality and employ heuristics to capture desired physical constraints.
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