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This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by…
Markov decision process over vector addition system with states (VASS MDP) is a finite state model combining non-deterministic and probabilistic behavior, augmented with non-negative integer counters that can be incremented or decremented…
We consider the problem of controlling a fully specified Markov decision process (MDP), also known as the planning problem, when the state space is very large and calculating the optimal policy is intractable. Instead, we pursue the more…
We study online learning in episodic constrained Markov decision processes (CMDPs), where the learner aims at collecting as much reward as possible over the episodes, while satisfying some long-term constraints during the learning process.…
We introduce and study constrained Markov Decision Processes (cMDPs) with anytime constraints. An anytime constraint requires the agent to never violate its budget at any point in time, almost surely. Although Markovian policies are no…
Stochastic domains often involve risk-averse decision makers. While recent work has focused on how to model risk in Markov decision processes using risk measures, it has not addressed the problem of solving large risk-averse formulations.…
Integrated task and motion planning has emerged as a challenging problem in sequential decision making, where a robot needs to compute high-level strategy and low-level motion plans for solving complex tasks. While high-level strategies…
Markov decision problems (MDPs) provide the foundations for a number of problems of interest to AI researchers studying automated planning and reinforcement learning. In this paper, we summarize results regarding the complexity of solving…
Non-stationary domains, that change in unpredicted ways, are a challenge for agents searching for optimal policies in sequential decision-making problems. This paper presents a combination of Markov Decision Processes (MDP) with Answer Set…
Robust Markov decision processes (MDPs) allow to compute reliable solutions for dynamic decision problems whose evolution is modeled by rewards and partially-known transition probabilities. Unfortunately, accounting for uncertainty in the…
Low-rank methods for semidefinite programming (SDP) have gained a lot of interest recently, especially in machine learning applications. Their analysis often involves determinant-based or Schatten-norm penalties, which are hard to implement…
In the decremental $(1+\epsilon)$-approximate Single-Source Shortest Path (SSSP) problem, we are given a graph $G=(V,E)$ with $n = |V|, m = |E|$, undergoing edge deletions, and a distinguished source $s \in V$, and we are asked to process…
This paper introduces a new robust interior point method analysis for semidefinite programming (SDP). This new robust analysis can be combined with either logarithmic barrier or hybrid barrier. Under this new framework, we can improve the…
We present improved deterministic algorithms for approximating shortest paths in the Congested Clique model of distributed computing. We obtain $poly(\log\log n)$-round algorithms for the following problems in unweighted undirected…
Many problems in sequential decision making and stochastic control often have natural multiscale structure: sub-tasks are assembled together to accomplish complex goals. Systematically inferring and leveraging hierarchical structure,…
We study the vertex-decremental Single-Source Shortest Paths (SSSP) problem: given an undirected graph $G=(V,E)$ with lengths $\ell(e)\geq 1$ on its edges and a source vertex $s$, we need to support (approximate) shortest-path queries in…
We propose a novel generalization of constrained Markov decision processes (CMDPs) that we call the \emph{semi-infinitely constrained Markov decision process} (SICMDP). Particularly, we consider a continuum of constraints instead of a…
Markov chains are the de facto finite-state model for stochastic dynamical systems, and Markov decision processes (MDPs) extend Markov chains by incorporating non-deterministic behaviors. Given an MDP and rewards on states, a classical…
Markov Decision Processes (MDPs) are a formal framework for modeling and solving sequential decision-making problems. In finite-time horizons such problems are relevant for instance for optimal stopping or specific supply chain problems,…
Calculating optimal policies is known to be computationally difficult for Markov decision processes (MDPs) with Borel state and action spaces. This paper studies finite-state approximations of discrete time Markov decision processes with…