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The uniform quadratic optimizatin problem (UQ) is a nonconvex quadratic constrained quadratic programming (QCQP) sharing the same Hessian matrix. Based on the second-order cone programming (SOCP) relaxation, we establish a new sufficient…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…
We consider the problem of learning by demonstration from agents acting in unknown stochastic Markov environments or games. Our aim is to estimate agent preferences in order to construct improved policies for the same task that the agents…
In this paper, we consider the problem of minimizing a difference-of-convex objective over a nonlinear conic constraint, where the cone is closed, convex, pointed and has a nonempty interior. We assume that the support function of a compact…
Optimal control and sequential decision making are widely used in many complex tasks. Optimal control over a sequence of natural images is a first step towards understanding the role of vision in control. Here, we formalize this problem as…
We study learning problems involving arbitrary classes of functions $F$, distributions $X$ and targets $Y$. Because proper learning procedures, i.e., procedures that are only allowed to select functions in $F$, tend to perform poorly unless…
The development of machine learning algorithms has been gathering relevance to address the increasing modelling complexity of manufacturing decision-making problems. Reinforcement learning is a methodology with great potential due to the…
The response envelope model provides substantial efficiency gains over the standard multivariate linear regression by identifying the material part of the response to the model and by excluding the immaterial part. In this paper, we propose…
This paper presents a piecewise convexification method for solving non-convex multi-objective optimization problems with box constraints. Based on the ideas of the $\alpha$-based Branch and Bound (${\rm \alpha BB}$) method of global…
Stochastic approximation is a foundation for many algorithms found in machine learning and optimization. It is in general slow to converge: the mean square error vanishes as $O(n^{-1})$. A deterministic counterpart known as quasi-stochastic…
We study a Q learning algorithm for continuous time stochastic control problems. The proposed algorithm uses the sampled state process by discretizing the state and control action spaces under piece-wise constant control processes. We show…
Reinforcement Learning (RL) techniques have been increasingly applied in optimizing control systems. However, their application in quantum systems is hampered by the challenge of performing closed-loop control due to the difficulty in…
We consider the problem of synthesizing optimal linear feedback policies subject to arbitrary convex constraints on the feedback matrix. This is known to be a hard problem in the usual formulations ($\Htwo,\Hinf,\LQR$) and previous works…
Q-learning methods represent a commonly used class of algorithms in reinforcement learning: they are generally efficient and simple, and can be combined readily with function approximators for deep reinforcement learning (RL). However, the…
We consider the question of estimating a solution to a system of equations that involve convex nonlinearities, a problem that is common in machine learning and signal processing. Because of these nonlinearities, conventional estimators…
Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…
We present the viewpoint that optimization problems encountered in machine learning can often be interpreted as minimizing a convex functional over a function space, but with a non-convex constraint set introduced by model parameterization.…
When deploying artificial agents in real-world environments where they interact with humans, it is crucial that their behavior is aligned with the values, social norms or other requirements of that environment. However, many environments…
We describe an approximate dynamic programming method for stochastic control problems on infinite state and input spaces. The optimal value function is approximated by a linear combination of basis functions with coefficients as decision…
This paper presents a strictly convex chance-constrained stochastic control framework that accounts for uncertainty in control specifications such as reference trajectories and operational constraints. By jointly optimizing control inputs…