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In this paper, we consider planning in stochastic shortest path (SSP) problems, a subclass of Markov Decision Problems (MDP). We focus on medium-size problems whose state space can be fully enumerated. This problem has numerous important…
A large class of decision making under uncertainty problems can be described via Markov decision processes (MDPs) or partially observable MDPs (POMDPs), with application to artificial intelligence and operations research, among others.…
This paper introduces OptimizedDP, a high-performance software library for several common grid-based dynamic programming (DP) algorithms used in control theory and robotics. Specifically, OptimizedDP provides functions to numerically solve…
The paper investigates stochastic resource allocation problems with scarce, reusable resources and non-preemtive, time-dependent, interconnected tasks. This approach is a natural generalization of several standard resource management…
We consider the fixed-delay synthesis problem for continuous-time Markov chains extended with fixed-delay transitions (fdCTMC). The goal is to synthesize concrete values of the fixed-delays (timeouts) that minimize the expected total cost…
In this paper, we develop a method to automatically generate a control policy for a dynamical system modeled as a Markov Decision Process (MDP). The control specification is given as a Linear Temporal Logic (LTL) formula over a set of…
Planning problems are hard, motion planning, for example, isPSPACE-hard. Such problems are even more difficult in the presence of uncertainty. Although, Markov Decision Processes (MDPs) provide a formal framework for such problems, finding…
Boolean MaxSAT, as well as generalized formulations such as Min-MaxSAT and Max-hybrid-SAT, are fundamental optimization problems in Boolean reasoning. Existing methods for MaxSAT have been successful in solving benchmarks in CNF format.…
Semidefinite programming (SDP) is a fundamental convex optimization problem with wide-ranging applications. However, solving large-scale instances remains computationally challenging due to the high cost of solving linear systems and…
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies…
Dynamic optimization problems involving discrete decisions have several applications, yet lead to challenging optimization problems that must be addressed efficiently. Combining discrete variables with potentially nonlinear constraints…
Partially observable Markov decision processes (POMDPs) provide an elegant mathematical framework for modeling complex decision and planning problems in stochastic domains in which states of the system are observable only indirectly, via a…
Robust Markov decision processes (RMDPs) extend standard Markov decision processes (MDPs) to account for uncertainty in the transition probabilities. RMDPs have an uncertainty set that defines a set of possible transition functions, each of…
Decentralized partially observable Markov decision processes (Dec-POMDPs) are rich models for cooperative decision-making under uncertainty, but are often intractable to solve optimally (NEXP-complete). The transition and observation…
In this paper we provide faster algorithms for approximately solving discounted Markov Decision Processes in multiple parameter regimes. Given a discounted Markov Decision Process (DMDP) with $|S|$ states, $|A|$ actions, discount factor…
Markov Decision Processes (MDPs) are a mathematical framework for modeling sequential decision making under uncertainty. The classical approaches for solving MDPs are well known and have been widely studied, some of which rely on…
Dynamic Mode Decomposition (DMD) is an unsupervised machine learning method that has attracted considerable attention in recent years owing to its equation-free structure, ability to easily identify coherent spatio-temporal structures in…
Multi-agent planning in stochastic environments can be framed formally as a decentralized Markov decision problem. Many real-life distributed problems that arise in manufacturing, multi-robot coordination and information gathering scenarios…
In the field of Sequential Decision Making (SDM), two paradigms have historically vied for supremacy: Automated Planning (AP) and Reinforcement Learning (RL). In the spirit of reconciliation, this article reviews AP, RL and hybrid methods…
This paper presents two new approaches to decomposing and solving large Markov decision problems (MDPs), a partial decoupling method and a complete decoupling method. In these approaches, a large, stochastic decision problem is divided into…