Optimality and Suboptimality of MPPI Control in Stochastic and Deterministic Settings
Model predictive path integral (MPPI) control has recently received a lot of attention, especially in the robotics and reinforcement learning communities. This letter aims to make the MPPI control framework more accessible to the optimal control community. We present three classes of optimal control problems and their solutions by MPPI. Further, we investigate the suboptimality of MPPI to general deterministic nonlinear discrete-time systems. Here, suboptimality is defined as the deviation between the control provided by MPPI and the optimal solution to the deterministic optimal control problem. Our findings are that in a smooth and unconstrained setting, the growth of suboptimality in the control input trajectory is second-order with the scaling of uncertainty. The results indicate that the suboptimality of the MPPI solution can be modulated by appropriately tuning the hyperparameters. We illustrate our findings using numerical examples.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
The Price of Adaptivity in Stochastic Convex Optimization
We prove impossibility results for adaptivity in non-smooth stochastic convex optimization. Given a set of problem parameters we wish to adapt to, we define a "price of adaptivity" (PoA) that, roughly speaking, measures …
LC-Tsallis-INF: Generalized Best-of-Both-Worlds Linear Contextual Bandits
This study considers the linear contextual bandit problem with independent and identically distributed (i.i.d.) contexts. In this problem, existing studies have proposed Best-of-Both-Worlds (BoBW) algorithms whose regret…
Multi-Armed BanditsGauss-Newton accelerated MPPI Control
Model Predictive Path Integral (MPPI) control is a sampling-based optimization method that has recently attracted attention, particularly in the robotics and reinforcement learning communities. MPPI has been widely appli…
Computational EfficiencyReinforcement LearningImproving the Convergence Rates of Forward Gradient Descent with Repeated Sampling
Forward gradient descent (FGD) has been proposed as a biologically more plausible alternative of gradient descent as it can be computed without backward pass. Considering the linear model with $d$ parameters, previous wo…
Implicit Dual-Control for Visibility-Aware Navigation in Unstructured Environments
Navigating complex, cluttered, and unstructured environments that are a priori unknown presents significant challenges for autonomous ground vehicles, particularly when operating with a limited field of view(FOV) resulti…