Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userSOS: Safe, Optimal and Small Strategies for Hybrid Markov Decision Processes
198
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
For hybrid Markov decision processes, UPPAAL Stratego can compute strategies that are safe for a given safety property and (in the limit) optimal for a given cost function. Unfortunately, these strategies cannot be exported easily since they are computed as a very long list. In this paper, we demonstrate methods to learn compact representations of the strategies in the form of decision trees. These decision trees are much smaller, more understandable, and can easily be exported as code that can be loaded into embedded systems. Despite the size compression and actual differences to the original strategy, we provide guarantees on both safety and optimality of the decision-tree strategy. On the top, we show how to obtain yet smaller representations, which are still guaranteed safe, but achieve a desired trade-off between size and optimality.
rate research
Read More
We study reinforcement learning for the optimal control of Branching Markov Decision Processes (BMDPs), a natural extension of (multitype) Branching Markov Chains (BMCs). The state of a (discrete-time) BMCs is a collection of entities of various types that, while spawning other entities, generate a payoff. In comparison with BMCs, where the evolution of a each entity of the same type follows the same probabilistic pattern, BMDPs allow an external controller to pick from a range of options. This permits us to study the best/worst behaviour of the system. We generalise model-free reinforcement learning techniques to compute an optimal control strategy of an unknown BMDP in the limit. We present results of an implementation that demonstrate the practicality of the approach.
In this paper, we consider the problem of controlling a partially observed Markov decision process (POMDP) in order to actively estimate its state trajectory over a fixed horizon with minimal uncertainty. We pose a novel active smoothing problem in which the objective is to directly minimise the smoother entropy, that is, the conditional entropy of the (joint) state trajectory distribution of concern in fixed-interval Bayesian smoothing. Our formulation contrasts with prior active approaches that minimise the sum of conditional entropies of the (marginal) state estimates provided by Bayesian filters. By establishing a novel form of the smoother entropy in terms of the POMDP belief (or information) state, we show that our active smoothing problem can be reformulated as a (fully observed) Markov decision process with a value function that is concave in the belief state. The concavity of the value function is of particular importance since it enables the approximate solution of our active smoothing problem using piecewise-linear function approximations in conjunction with standard POMDP solvers. We illustrate the approximate solution of our active smoothing problem in simulation and compare its performance to alternative approaches based on minimising marginal state estimate uncertainties.
We consider Markov decision processes (MDP) as generators of sequences of probability distributions over states. A probability distribution is p-synchronizing if the probability mass is at least p in a single state, or in a given set of states. We consider four temporal synchronizing modes: a sequence of probability distributions is always p-synchronizing, eventually p-synchronizing, weakly p-synchronizing, or strongly p-synchronizing if, respectively, all, some, infinitely many, or all but finitely many distributions in the sequence are p-synchronizing. For each synchronizing mode, an MDP can be (i) sure winning if there is a strategy that produces a 1-synchronizing sequence; (ii) almost-sure winning if there is a strategy that produces a sequence that is, for all epsilon > 0, a (1-epsilon)-synchronizing sequence; (iii) limit-sure winning if for all epsilon > 0, there is a strategy that produces a (1-epsilon)-synchronizing sequence. We provide fundamental results on the expressiveness, decidability, and complexity of synchronizing properties for MDPs. For each synchronizing mode, we consider the problem of deciding whether an MDP is sure, almost-sure, or limit-sure winning, and we establish matching upper and lower complexity bounds of the problems: for all winning modes, we show that the problems are PSPACE-complete for eventually and weakly synchronizing, and PTIME-complete for always and strongly synchronizing. We establish the memory requirement for winning strategies, and we show that all winning modes coincide for always synchronizing, and that the almost-sure and limit-sure winning modes coincide for weakly and strongly synchronizing.
In this work, we study the problem of actively classifying the attributes of dynamical systems characterized as a finite set of Markov decision process (MDP) models. We are interested in finding strategies that actively interact with the dynamical system and observe its reactions so that the attribute of interest is classified efficiently with high confidence. We present a decision-theoretic framework based on partially observable Markov decision processes (POMDPs). The proposed framework relies on assigning a classification belief (a probability distribution) to the attributes of interest. Given an initial belief, confidence level over which a classification decision can be made, a cost bound, safe belief sets, and a finite time horizon, we compute POMDP strategies leading to classification decisions. We present two different algorithms to compute such strategies. The first algorithm computes the optimal strategy exactly by value iteration. To overcome the computational complexity of computing the exact solutions, we propose a second algorithm is based on adaptive sampling to approximate the optimal probability of reaching a classification decision. We illustrate the proposed methodology using examples from medical diagnosis and privacy-preserving advertising.
In this work we present a multi-armed bandit framework for online expert selection in Markov decision processes and demonstrate its use in high-dimensional settings. Our method takes a set of candidate expert policies and switches between them to rapidly identify the best performing expert using a variant of the classical upper confidence bound algorithm, thus ensuring low regret in the overall performance of the system. This is useful in applications where several expert policies may be available, and one needs to be selected at run-time for the underlying environment.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
