Parameterized Convex Minorant for Objective Function Approximation in Amortized Optimization
Parameterized convex minorant (PCM) method is proposed for the approximation of the objective function in amortized optimization. In the proposed method, the objective function approximator is expressed by the sum of a PCM and a nonnegative gap function, where the objective function approximator is bounded from below by the PCM convex in the optimization variable. The proposed objective function approximator is a universal approximator for continuous functions, and the global minimizer of the PCM attains the global minimum of the objective function approximator. Therefore, the global minimizer of the objective function approximator can be obtained by a single convex optimization. As a realization of the proposed method, extended parameterized log-sum-exp network is proposed by utilizing a parameterized log-sum-exp network as the PCM. Numerical simulation is performed for parameterized non-convex objective function approximation and for learning-based nonlinear model predictive control to demonstrate the performance and characteristics of the proposed method. The simulation results support that the proposed method can be used to learn objective functions and to find a global minimizer reliably and quickly by using convex optimization algorithms.
Code (1)
Tasks
Model Predictive ControlSimilar Papers 제목 키워드 기반
Enhanced Low-Rank Matrix Approximation
This letter proposes to estimate low-rank matrices by formulating a convex optimization problem with non-convex regularization. We employ parameterized non-convex penalty functions to estimate the non-zero singular value…
DenoisingImage DenoisingSuccessive Convex Approximation Based Off-Policy Optimization for Constrained Reinforcement Learning
We propose a successive convex approximation based off-policy optimization (SCAOPO) algorithm to solve the general constrained reinforcement learning problem, which is formulated as a constrained Markov decision process …
reinforcement-learningReinforcement Learning (RL)Convergence rates of the stochastic alternating algorithm for bi-objective optimization
Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consi…
validLevel-Set Methods for Finite-Sum Constrained Convex Optimization
We consider the constrained optimization where the objective function and the constraints are defined as summation of finitely many loss functions. This model has applications in machine learning such as Neyman-Pear…
Parameterized Convex Universal Approximators for Decision-Making Problems
Parameterized max-affine (PMA) and parameterized log-sum-exp (PLSE) networks are proposed for general decision-making problems. The proposed approximators generalize existing convex approximators, namely, max-affine (MA)…
Decision Making