Stochastic Shortest Path with Energy Constraints in POMDPs

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard constraint. The energy levels may increase and decrease with transitions, and the hard constraint requires that the energy level must remain positive in all steps till the target is reached. First, we present a novel algorithm for solving POMDPs with energy levels, developing on existing POMDP solvers and using RTDP as its main method. Our second contribution is related to policy representation. For larger POMDP instances the policies computed by existing solvers are too large to be understandable. We present an automated procedure based on machine learning techniques that automatically extracts important decisions of the policy allowing us to compute succinct human readable policies. Finally, we show experimentally that our algorithm performs well and computes succinct policies on a number of POMDP instances from the literature that were naturally enhanced with energy levels.Comment: Technical report accompanying a paper published in proceedings of AAMAS 201

Planning in POMDPs Using Multiplicity Automata

Planning and learning in Partially Observable MDPs (POMDPs) are among the most challenging tasks in both the AI and Operation Research communities. Although solutions to these problems are intractable in general, there might be special cases, such as structured POMDPs, which can be solved efficiently. A natural and possibly efficient way to represent a POMDP is through the predictive state representation (PSR) - a representation which recently has been receiving increasing attention. In this work, we relate POMDPs to multiplicity automata- showing that POMDPs can be represented by multiplicity automata with no increase in the representation size. Furthermore, we show that the size of the multiplicity automaton is equal to the rank of the predictive state representation. Therefore, we relate both the predictive state representation and POMDPs to the well-founded multiplicity automata literature. Based on the multiplicity automata representation, we provide a planning algorithm which is exponential only in the multiplicity automata rank rather than the number of states of the POMDP. As a result, whenever the predictive state representation is logarithmic in the standard POMDP representation, our planning algorithm is efficient.Comment: Appears in Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence (UAI2005

Learning to Represent Haptic Feedback for Partially-Observable Tasks

The sense of touch, being the earliest sensory system to develop in a human body [1], plays a critical part of our daily interaction with the environment. In order to successfully complete a task, many manipulation interactions require incorporating haptic feedback. However, manually designing a feedback mechanism can be extremely challenging. In this work, we consider manipulation tasks that need to incorporate tactile sensor feedback in order to modify a provided nominal plan. To incorporate partial observation, we present a new framework that models the task as a partially observable Markov decision process (POMDP) and learns an appropriate representation of haptic feedback which can serve as the state for a POMDP model. The model, that is parametrized by deep recurrent neural networks, utilizes variational Bayes methods to optimize the approximate posterior. Finally, we build on deep Q-learning to be able to select the optimal action in each state without access to a simulator. We test our model on a PR2 robot for multiple tasks of turning a knob until it clicks.Comment: IEEE International Conference on Robotics and Automation (ICRA), 201