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We consider the problem of optimizing the economic performance of nonlinear constrained systems subject to uncertain time-varying parameters and bounded disturbances. In particular, we propose an adaptive economic model predictive control…

We study an optimal liquidation problem under the ambiguity with respect to price impact parameters. Our main results show that the value function and the optimal trading strategy can be characterized by the solution to a semi-linear PDE…

We study the positive-definiteness of a family of $L^2(\mathbf{R})$ integral operators with kernel $K_{t, a}(x, y) = (1 + (x - y)^2 + a(x^2 + y^2)^t)^{-1}$, with $t > 0$ and $a > 0$. When $0 < t \le 1$, the known theory of positive-definite…

In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a $K$-invariant measure $\mu$ with full support, we show that conditional positive…

We consider a symmetric matrix, the entries of which depend linearly on some parameters. The domains of the parameters are compact real intervals. We investigate the problem of checking whether for each (or some) setting of the parameters,…

We study optimal solutions to an abstract optimization problem for measures, which is a generalization of classical variational problems in information theory and statistical physics. In the classical problems, information and relative…

Performative distribution shift captures the setting where the choice of which ML model is deployed changes the data distribution. For example, a bank which uses the number of open credit lines to determine a customer's risk of default on a…

We propose a principled kernel-based policy iteration algorithm to solve the continuous-state Markov Decision Processes (MDPs). In contrast to most decision-theoretic planning frameworks, which assume fully known state transition models, we…

The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…

Long term optimal investment problems are studied in a factor model with matrix valued state variables. Explicit parameter restrictions are obtained under which, for an isoelastic investor, the finite horizon value function and optimal…

This paper studies convex duality in optimal investment and contingent claim valuation in markets where traded assets may be subject to nonlinear trading costs and portfolio constraints. Under fairly general conditions, the dual expressions…

Kernel methods are versatile tools for function approximation and surrogate modeling. In particular, greedy techniques offer computational efficiency and reliability through inherent sparsity and provable convergence. Inspired by the…

In this paper, we propose a data-adaptive non-parametric kernel learning framework in margin based kernel methods. In model formulation, given an initial kernel matrix, a data-adaptive matrix with two constraints is imposed in an entry-wise…

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…

The classical discrete time model of proportional transaction costs relies on the assumption that a feasible portfolio process has solvent increments at each step. We extend this setting in two directions, allowing for convex transaction…

Classifiers and rating scores are prone to implicitly codifying biases, which may be present in the training data, against protected classes (i.e., age, gender, or race). So it is important to understand how to design classifiers and scores…

We study positive definite kernels pulled back along a finite family of self-maps under a subinvariance inequality for the associated branching operator. Iteration produces an increasing kernel tower with defect kernels. Under diagonal…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…