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We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…
Trajectory prediction is a pivotal component of autonomous driving systems, enabling the application of accumulated movement experience to current scenarios. Although most existing methods concentrate on learning continuous representations…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
We propose model predictive funnel control, a novel model predictive control (MPC) scheme building upon recent results in funnel control. The latter is a high-gain feedback methodology that achieves evolution of the measured output within…
Foundation models have revolutionized general-purpose problem-solving, offering rapid task adaptation through pretraining, meta-training, and finetuning. Recent crucial advances in these paradigms reveal the importance of challenging task…
We consider the PDE-constrained optimal control of a leader-follower kinetic opinion formation model, with a Fokker-Planck-type system of partial differential equations as a state constraint. We derive the Boltzmann-type and…
Reactive point processes (RPPs) are a new statistical model designed for predicting discrete events in time based on past history. RPPs were developed to handle an important problem within the domain of electrical grid reliability:…
Optimal control problems of forward-backward stochastic Volterra integral equations (FBSVIEs, in short) with closed control regions are formulated and studied. Instead of using spike variation method as one may imagine, here we turn to…
Training neural networks on randomly generated artificial datasets yields Bayesian models that capture the prior defined by the dataset-generating distribution. Prior-data Fitted Networks (PFNs) are a class of methods designed to leverage…
Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…
Preferences play a key role in determining what goals/constraints to satisfy when not all constraints can be satisfied simultaneously. In this work, we study preference-based planning in a stochastic system modeled as a Markov decision…
Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A…
Markov Decision Processes (MDPs) have been used to formulate many decision-making problems in science and engineering. The objective is to synthesize the best decision (action selection) policies to maximize expected rewards (or minimize…
The inherent flexibility of soft robots offers numerous advantages, such as enhanced adaptability and improved safety. However, this flexibility can also introduce challenges regarding highly uncertain and nonlinear motion. These challenges…
Time series forecasting underpins vital decision-making across various sectors, yet raw predictions from sophisticated models often harbor systematic errors and biases. We examine the Forecast-Then-Optimize (FTO) framework, pioneering its…
The paper investigates data-driven output-feedback predictive control of linear systems subject to stochastic disturbances. The scheme relies on the recursive solution of a suitable data-driven reformulation of a stochastic Optimal Control…
We study methods for solving stochastic control problems of systems of forward-backward mean-field equations with delay, in finite or infinite horizon. Necessary and sufficient maximum principles under partial information are given. The…
Conventional reinforcement learning (RL) methods can successfully solve a wide range of sequential decision problems. However, learning policies that can generalize predictably across multiple tasks in a setting with non-Markovian reward…
Policy evaluation is central to economic data analysis, but economists mostly work with observational data in view of limited opportunities to carry out controlled experiments. In the potential outcome framework, the panel data approach…
Expanding the ideas of the author's paper 'Nonexpansive maps and option pricing theory' (Kibernetica 34:6 (1998), 713-724) we develop a pure game-theoretic approach to option pricing, by-passing stochastic modeling. Risk neutral…