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Stochastic balancing domain decomposition by constraints (BDDC) algorithms are developed and analyzed for the sampling of the solutions of linear stochastic elliptic equations with random coefficients. Different from the deterministic BDDC…
Differential Dynamic Programming (DDP) is a popular technique used to generate motion for dynamic-legged robots in the recent past. However, in most cases, only the first-order partial derivatives of the underlying dynamics are used,…
Accurate forecasting of industrial time series requires balancing predictive accuracy with physical plausibility under non-stationary operating conditions. Existing data-driven models often achieve strong statistical performance but…
Markov decision processes (MDPs) are a popular model for performance analysis and optimization of stochastic systems. The parameters of stochastic behavior of MDPs are estimates from empirical observations of a system; their values are not…
Spike-timing-dependent plasticity(STDP) is a biological process of synaptic modification caused by the difference of firing order and timing between neurons. One of the neurodynamical roles of STDP is to form a macroscopic geometrical…
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…
The abstraction of dynamical systems is a powerful tool that enables the design of feedback controllers using a correct-by-design framework. We investigate a novel scheme to obtain data-driven abstractions of discrete-time stochastic…
We tackle the problem of conditioning probabilistic programs on distributions of observable variables. Probabilistic programs are usually conditioned on samples from the joint data distribution, which we refer to as deterministic…
Since the introduction of the Black-Scholes model stochastic processes have played an increasingly important role in mathematical finance. In many cases prices, volatility and other quantities can be modeled using stochastic ordinary…
Today's complex robotic designs comprise in some cases a large number of degrees of freedom, enabling for multi-objective task resolution (e.g., humanoid robots or aerial manipulators). This paper tackles the stability problem of a…
Multi-stage stochastic optimization lies at the core of decision-making under uncertainty. As the analytical solution is available only in exceptional cases, dynamic optimization aims to efficiently find approximations but often neglects…
The Markov decision process (MDP) formulation used to model many real-world sequential decision making problems does not efficiently capture the setting where the set of available decisions (actions) at each time step is stochastic.…
Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined…
Driven by ambitious renewable portfolio standards, large-scale inclusion of variable energy resources (such as wind and solar) are expected to introduce unprecedented levels of uncertainty into power system operations. The current practice…
Stochastic programming can be applied to consider uncertainties in energy system optimization models for capacity expansion planning. However, these models become increasingly large and time-consuming to solve, even without considering…
Most decision-focused learning work has focused on single stage problems whereas many real-world decision problems are more appropriately modelled using multistage optimisation. In multistage problems contextual information is revealed over…
The aim of this paper is to address optimality of stochastic control strategies via dynamic programming subject to total variation distance ambiguity on the conditional distribution of the controlled process. We formulate the stochastic…
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions ("dynamic programming") or scenario trees ("stochastic programming") to approximate the impact of a…
Discrete-time stochastic systems with continuous spaces are hard to verify and control, even with MDP abstractions due to the curse of dimensionality. We propose an abstraction-based framework with robust dynamic programming mappings that…
We propose a new financial model, the stochastic volatility model with sticky drawdown and drawup processes (SVSDU model), which enables us to capture the features of winning and losing streaks that are common across financial markets but…