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Optimal control (OC) algorithms such as Differential Dynamic Programming (DDP) take advantage of the derivatives of the dynamics to efficiently control physical systems. Yet, in the presence of nonsmooth dynamical systems, such class of…
Dual control denotes a class of control problems where the parameters governing the system are imperfectly known. The challenge is to find the optimal balance between probing, i.e. exciting the system to understand it more, and caution,…
Regularization techniques are widely employed in optimization-based approaches for solving ill-posed inverse problems in data analysis and scientific computing. These methods are based on augmenting the objective with a penalty function,…
Distributed training of $l_1$ regularized classifiers has received great attention recently. Most existing methods approach this problem by taking steps obtained from approximating the objective by a quadratic approximation that is…
Typical reinforcement learning (RL) methods show limited applicability for real-world industrial control problems because industrial systems involve various constraints and simultaneously require continuous and discrete control. To overcome…
We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…
Convergence guarantees for optimization over bounded-rank matrices are delicate to obtain because the feasible set is a non-smooth and non-convex algebraic variety. Existing techniques include projected gradient descent, fixed-rank…
We formulate pure characteristics demand models under uncertainties of probability distributions as distributionally robust mathematical programs with stochastic complementarity constraints (DRMP-SCC). For any fixed first-stage variable and…
Dynamic portfolio optimization is the process of sequentially allocating wealth to a collection of assets in some consecutive trading periods, based on investors' return-risk profile. Automating this process with machine learning remains a…
This paper studies the ubiquitous problem of liquidating large quantities of highly correlated stocks, a task frequently encountered by institutional investors and proprietary trading firms. Traditional methods in this setting suffer from…
We study the problem of optimal risk policies and dividend strategies for an insurance company operating under the constraint that the timing of shareholder payouts is governed by the arrival times of a Poisson process. Concurrently, risk…
We consider a two-dimensional optimal dividend problem in the context of two insurance companies with compound Poisson surplus processes, who collaborate by paying each other's deficit when possible. We solve the stochastic control problem…
In this paper, we consider the problem of distributed optimisation of a separable convex cost function over a graph, where every edge and node in the graph could carry both linear equality and/or inequality constraints. We show how to…
Distributed algorithms for solving coupled semidefinite programs (SDPs) commonly require many iterations to converge. They also put high computational demand on the computational agents. In this paper we show that in case the coupled…
This paper considers linear-quadratic control of a non-linear dynamical system subject to arbitrary cost. I show that for this class of stochastic control problems the non-linear Hamilton-Jacobi-Bellman equation can be transformed into a…
This paper introduces a novel Differential Dynamic Programming (DDP) algorithm for solving discrete-time finite-horizon optimal control problems with inequality constraints. Two variants, namely Feasible- and Infeasible-IPDDP algorithms,…
Dynamic hedging is the practice of periodically transacting financial instruments to offset the risk caused by an investment or a liability. Dynamic hedging optimization can be framed as a sequential decision problem; thus, Reinforcement…
Recently, a number of learning-based optimization methods that combine data-driven architectures with the classical optimization algorithms have been proposed and explored, showing superior empirical performance in solving various ill-posed…
In this paper we consider a general, challenging distributed optimization set-up arising in several important network control applications. Agents of a network want to minimize the sum of local cost functions, each one depending on a local…