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Planning in adversarial and uncertain environments can be modeled as the problem of devising strategies in stochastic perfect information games. These games are generalizations of Markov decision processes (MDPs): there are two…
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…
We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This…
We study a multi-agent mean field type control problem in discrete time where the agents aim to find a socially optimal strategy and where the state and action spaces for the agents are assumed to be continuous. The agents are only weakly…
We investigate planning in time-critical domains represented as Markov Decision Processes, showing that search based techniques can be a very powerful method for finding close to optimal plans. To reduce the computational cost of planning…
Approximate dynamic programming is a popular method for solving large Markov decision processes. This paper describes a new class of approximate dynamic programming (ADP) methods- distributionally robust ADP-that address the curse of…
In this thesis we study adaptive nonparametric regression with noise misspecification and the complexity of approximation of random fields in dependence of the dimension. First, we consider the problem of pointwise estimation in…
This paper considers a multi-agent Markov Decision Process (MDP), where there are $n$ agents and each agent $i$ is associated with a state $s_i$ and action $a_i$ taking values from a finite set. Though the global state space size and action…
Markov decision processes are a ubiquitous formalism for modelling systems with non-deterministic and probabilistic behavior. Verification of these models is subject to the famous state space explosion problem. We alleviate this problem by…
Multi-agent planning under stochastic dynamics is usually formalised using decentralized (partially observable) Markov decision processes ( MDPs) and reachability or expected reward specifications. In this paper, we propose a different…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
Covert planning refers to a class of constrained planning problems where an agent aims to accomplish a task with minimal information leaked to a passive observer to avoid detection. However, existing methods of covert planning often…
Stochastic planning can be reduced to probabilistic inference in large discrete graphical models, but hardness of inference requires approximation schemes to be used. In this paper we argue that such applications can be disentangled along…
Stochastic approximation is a framework unifying many random iterative algorithms occurring in a diverse range of applications. The stability of the process is often difficult to verify in practical applications and the process may even be…
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion…
In this work we introduce new approximate similarity relations that are shown to be key for policy (or control) synthesis over general Markov decision processes. The models of interest are discrete-time Markov decision processes, endowed…
Theoretical approaches to binary-state models on complex networks are generally restricted to infinite size systems, where a set of non-linear deterministic equations is assumed to characterize its dynamics and stationary properties. We…
Recent research in decision theoretic planning has focussed on making the solution of Markov decision processes (MDPs) more feasible. We develop a family of algorithms for structured reachability analysis of MDPs that are suitable when an…
We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…
In recent years, individual-based/agent-based modeling has been applied to study a wide range of applications, ranging from engineering problems to phenomena in sociology, economics and biology. Simulating such agent-based models over…