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The development of ethical AI systems is currently geared toward setting objective functions that align with human objectives. However, finding such functions remains a research challenge, while in RL, setting rewards by hand is a fairly…

In this paper, we study a regularised relaxed optimal control problem and, in particular, we are concerned with the case where the control variable is of large dimension. We introduce a system of mean-field Langevin equations, the invariant…

The distribution of block maxima of sequences of independent and identically-distributed random variables is used to model extreme values in many disciplines. The traditional extreme value (EV) theory derives a closed-form expression for…

We present a comparison between two approaches to modelling hyperelastic material behaviour using data. The first approach is a novel approach based on Data-driven Computational Mechanics (DDCM) that completely bypasses the definition of a…

We consider the problem of dynamic buying and selling of shares from a collection of $N$ stocks with random price fluctuations. To limit investment risk, we place an upper bound on the total number of shares kept at any time. Assuming that…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

In this paper, we propose a new approach for stochastic control problems arising from utility maximization. The main idea is to directly start from the dynamical programming equation and compute the conditional expectation using a novel…

This paper presents a new theory, known as robust dynamic pro- gramming, for a class of continuous-time dynamical systems. Different from traditional dynamic programming (DP) methods, this new theory serves as a fundamental tool to analyze…

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the DDR model, each point is evolved via a nonlinear flow towards…

When a physical system is driven away from equilibrium, the statistical distribution of its dynamical trajectories informs many of its physical properties. Characterizing the nature of the distribution of dynamical observables, such as a…

In this paper, we propose a new design method of discrete-valued control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. We first formulate the discrete-valued control design as a…

This paper considers the problem of regulating a linear dynamical system to the solution of a convex optimization problem with an unknown or partially-known cost. We design a data-driven feedback controller - based on gradient flow dynamics…

We address the design and synthesis of optimal control strategies for high-dimensional stochastic dynamical systems. Such systems may be deterministic nonlinear systems evolving from random initial states, or systems driven by random…

In complex environments with large discrete action spaces, effective decision-making is critical in reinforcement learning (RL). Despite the widespread use of value-based RL approaches like Q-learning, they come with a computational burden,…

A key obstacle in automated analytics and meta-learning is the inability to recognize when different datasets contain measurements of the same variable. Because provided attribute labels are often uninformative in practice, this task may be…

Optimizing the learning rate remains a critical challenge in machine learning, essential for achieving model stability and efficient convergence. The Vector Auxiliary Variable (VAV) algorithm introduces a novel energy-based self-adjustable…

Over the recent past data-driven algorithms for solving stochastic optimal control problems in face of model uncertainty have become an increasingly active area of research. However, for singular controls and underlying diffusion dynamics…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

We study non-parametric estimation of choice models, which were introduced to alleviate unreasonable assumptions in traditional parametric models, and are prevalent in several application areas. Existing literature focuses only on the…

Data Darwinism (Part I) established a ten-level hierarchy for data processing, showing that stronger processing can unlock greater data value. However, that work relied on manually designed strategies for a single category. Modern…