Related papers: Capacities, Measurable Selection and Dynamic Progr…
Determinantal point processes (DPPs) are an important concept in random matrix theory and combinatorics. They have also recently attracted interest in the study of numerical methods for machine learning, as they offer an elegant "missing…
Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is also the foundation of reinforcement learning. In this paper,…
Data-Enabled Predictive Control (DeePC) bypasses the need for system identification by directly leveraging raw data to formulate optimal control policies. However, the size of the optimization problem in DeePC grows linearly with respect to…
In model selection problems for machine learning, the desire for a well-performing model with meaningful structure is typically expressed through a regularized optimization problem. In many scenarios, however, the meaningful structure is…
In this paper, we revisit the computation of controlled invariant sets for linear discrete-time systems through a trajectory-based viewpoint. We begin by introducing the notion of convex feasible points, which provides a new…
Meta continual learning algorithms seek to train a model when faced with similar tasks observed in a sequential manner. Despite promising methodological advancements, there is a lack of theoretical frameworks that enable analysis of…
The notion of a Moreau envelope is central to the analysis of first-order optimization algorithms for machine learning. Yet, it has not been developed and extended to be applied to a deep network and, more broadly, to a machine learning…
The multiple knapsack problem (MKP) generalizes the classical knapsack problem by assigning items to multiple knapsacks subject to capacity constraints. It is used to model many real-world resource allocation and scheduling problems. In…
Robust Model Predictive Control (MPC) for nonlinear systems is a problem that poses significant challenges as highlighted by the diversity of approaches proposed in the last decades. Often compromises with respect to computational load,…
We connect the study of pseudodeterministic algorithms to two major open problems about the structural complexity of $\mathsf{BPTIME}$: proving hierarchy theorems and showing the existence of complete problems. Our main contributions can be…
Dissipative particle dynamics (DPD) belongs to a class of models and computational algorithms developed to address mesoscale problems in complex fluids and soft matter in general. It is based on the notion of particles that represent…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…
The performance of an error correcting code is evaluated by its error probability, rate, and en/decoding complexity. The performance of a series of codes is evaluated by, as the block lengths approach infinity, whether their error…
Many real world problems naturally appear as constraints satisfaction problems (CSP), for which very efficient algorithms are known. Most of these involve the combination of two techniques: some direct propagation of constraints between…
We information-theoretically reformulate two measures of capacity from statistical learning theory: empirical VC-entropy and empirical Rademacher complexity. We show these capacity measures count the number of hypotheses about a dataset…
Motivated by the grid search method and Bayesian optimization, we introduce the concept of contractibility and its applications in model-based optimization. First, a basic framework of contraction methods is established to construct a…
Computers are deterministic dynamical systems (CHAOS 19:033124, 2009). Among other things, that implies that one should be able to use deterministic forecast rules to predict their behavior. That statement is sometimes-but not always-true.…
A general theory is developed to study individual based models which are discrete in time. We begin by constructing a Markov chain model that converges to a one-dimensional map in the infinite population limit. Stochastic fluctuations are…
Multi-stage decision problems under uncertainty can be efficiently solved with the Stochastic Dual Dynamic Programming (SDDP) algorithm. However, traditional implementations require all stage problems to be feasible. Feasibility is usually…
Parameter control aims at realizing performance gains through a dynamic choice of the parameters which determine the behavior of the underlying optimization algorithm. In the context of evolutionary algorithms this research line has for a…