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We study the problem of safe online convex optimization, where the action at each time step must satisfy a set of linear safety constraints. The goal is to select a sequence of actions to minimize the regret without violating the safety…

We study the asymptotic behavior of solutions to linear-quadratic mean field stochastic optimal control problems. By formulating an ergodic control framework, we characterize the convergence between the finite time horizon control problem…

We present a novel probabilistic approach for optimal path experimental design. In this approach a discrete path optimization problem is defined on a static navigation mesh, and trajectories are modeled as random variables governed by a…

In this paper, we consider reinforcement learning of Markov Decision Processes (MDP) with peak constraints, where an agent chooses a policy to optimize an objective and at the same time satisfy additional constraints. The agent has to take…

This paper investigates the problem of leadership development for an external influencer using the Friedkin-Johnsen (FJ) opinion dynamics model, where the influencer is modeled as a fully stubborn agent and leadership is quantified by…

We introduce a new framework for web page ranking -- reinforcement ranking -- that improves the stability and accuracy of Page Rank while eliminating the need for computing the stationary distribution of random walks. Instead of relying on…

We consider mixed-integer quadratic optimization problems with banded matrices and indicator variables. These problems arise pervasively in statistical inference problems with time-series data, where the banded matrix captures the temporal…

We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…

This work considers artificial feed-forward neural networks as parametric approximators in optimal control of discrete-time systems. Two different approaches are introduced to take polytopic input constraints into account. The first…

Optimal control of switched systems is challenging due to the discrete nature of the switching control input. The embedding-based approach addresses this challenge by solving a corresponding relaxed optimal control problem with only…

Decision-making under uncertainty is a critical aspect of many practical autonomous systems due to incomplete information. Partially Observable Markov Decision Processes (POMDPs) offer a mathematically principled framework for formulating…

We consider the constrained optimal control problem for the gradual-impulsive CTMDP model with the performance criteria being the expected total undiscounted costs (from the running cost and the cost from each time an impulse being…

Despite the empirical success of the actor-critic algorithm, its theoretical understanding lags behind. In a broader context, actor-critic can be viewed as an online alternating update algorithm for bilevel optimization, whose convergence…

The outcome of interactions in many real-world systems can be often explained by a hierarchy between the participants. Discovering hierarchy from a given directed network can be formulated as follows: partition vertices into levels such…

Trajectory optimization is a fundamental problem in robotics. While optimization of continuous control trajectories is well developed, many applications require both discrete and continuous, i.e., hybrid, controls. Finding an optimal…

This work proposes an open-loop methodology to solve chance constrained stochastic optimal control problems for linear systems with a stochastic control matrix. We consider a joint chance constraint for polytopic time-varying target sets…

This paper addresses the portfolio selection problem for nonlinear law-dependent preferences in continuous time, which inherently exhibit time inconsistency. Employing the method of stochastic maximum principle, we establish verification…

In this work we are interested in the modelling and control of opinion dynamics spreading on a time evolving network with scale-free asymptotic degree distribution. The mathematical model is formulated as a coupling of an opinion alignment…

This paper is concerned with the solution of the optimal stopping problem associated to the valuation of Perpetual American options driven by continuous time Markov chains. We introduce a new dynamic approach for the numerical pricing of…

Personalized PageRank (PPR) has enormous applications, such as link prediction and recommendation systems for social networks, which often require the fully PPR to be known. Besides, most of real-life graphs are edge-weighted, e.g., the…