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We consider a basic one-dimensional model of diffusion which allows to obtain a diversity of diffusive regimes whose speed depends on the moments of the per-site trapping time. This model is closely related to the continuous time random…
Risk management is particularly concerned with extreme events, but analysing these events is often hindered by the scarcity of data, especially in a multivariate context. This data scarcity complicates risk management efforts. Various tools…
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…
This thesis is devoted to the study of extreme value statistics in stochastic processes and their applications. In the first part, we obtain exact analytical results on the extreme value statistics of both discrete-time and continuous-time…
Despite broad interest in self-organizing systems, there are few quantitative, experimentally-applicable criteria for self-organization. The existing criteria all give counter-intuitive results for important cases. In this Letter, we…
A new method for stochastic control based on neural networks and using randomisation of discrete random variables is proposed and applied to optimal stopping time problems. The method models directly the policy and does not need the…
Modern self-driving autonomy systems heavily rely on deep learning. As a consequence, their performance is influenced significantly by the quality and richness of the training data. Data collecting platforms can generate many hours of raw…
A key question in clinical practice is accurate prediction of patient prognosis. To this end, nowadays, physicians have at their disposal a variety of tests and biomarkers to aid them in optimizing medical care. These tests are often…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
In the past few years, Online Convex Optimization (OCO) has received notable attention in the control literature thanks to its flexible real-time nature and powerful performance guarantees. In this paper, we propose new step-size rules and…
In this work, we present a novel robustness measure for continuous-time stochastic trajectories with respect to Signal Temporal Logic (STL) specifications. We show the soundness of the measure and develop a monitor for reasoning about…
It is well-known from the work of Kupper and Schachermayer that most law-invariant risk measures do not admit a time-consistent representation. In this work we show that in a Brownian filtration the "Optimized Certainty Equivalent" risk…
In this paper, a novel real-time acceleration-continuous path-constrained trajectory planning algorithm is proposed with an appealing built-in tradability mechanism between cruise motion and time-optimal motion. Different from existing…
A novel probabilistic numerical method for quantifying the uncertainty induced by the time integration of ordinary differential equations (ODEs) is introduced. Departing from the classical strategy to randomize ODE solvers by adding a…
By adopting a distributional viewpoint on law-invariant convex risk measures, we construct dynamics risk measures (DRMs) at the distributional level. We then apply these DRMs to investigate Markov decision processes, incorporating latent…
We use one-step conditional risk mappings to formulate a risk averse version of a total cost problem on a controlled Markov process in discrete time infinite horizon. The nonnegative one step costs are assumed to be lower semi-continuous…
In this paper, we investigate dynamic optimization problems featuring both stochastic control and optimal stopping in a finite time horizon. The paper aims to develop new methodologies, which are significantly different from those of mixed…
In this experience report, we apply deep active learning to the field of design optimization to reduce the number of computationally expensive numerical simulations. We are interested in optimizing the design of structural components, where…
Decision-making pipelines are generally characterized by tradeoffs among various risk functions. It is often desirable to manage such tradeoffs in a data-adaptive manner. As we demonstrate, if this is done naively, state-of-the art…