28 research outputs found
Data-Driven Chance Constrained Optimization under Wasserstein Ambiguity Sets
We present a data-driven approach for distributionally robust chance
constrained optimization problems (DRCCPs). We consider the case where the
decision maker has access to a finite number of samples or realizations of the
uncertainty. The chance constraint is then required to hold for all
distributions that are close to the empirical distribution constructed from the
samples (where the distance between two distributions is defined via the
Wasserstein metric). We first reformulate DRCCPs under data-driven Wasserstein
ambiguity sets and a general class of constraint functions. When the
feasibility set of the chance constraint program is replaced by its convex
inner approximation, we present a convex reformulation of the program and show
its tractability when the constraint function is affine in both the decision
variable and the uncertainty. For constraint functions concave in the
uncertainty, we show that a cutting-surface algorithm converges to an
approximate solution of the convex inner approximation of DRCCPs. Finally, for
constraint functions convex in the uncertainty, we compare the feasibility set
with other sample-based approaches for chance constrained programs.Comment: A shorter version is submitted to the American Control Conference,
201
Stochastic MPC with Distributionally Robust Chance Constraints
In this paper we discuss distributional robustness in the context of
stochastic model predictive control (SMPC) for linear time-invariant systems.
We derive a simple approximation of the MPC problem under an additive zero-mean
i.i.d. noise with quadratic cost. Due to the lack of distributional
information, chance constraints are enforced as distributionally robust (DR)
chance constraints, which we opt to unify with the concept of probabilistic
reachable sets (PRS). For Wasserstein ambiguity sets, we propose a simple
convex optimization problem to compute the DR-PRS based on finitely many
disturbance samples. The paper closes with a numerical example of a double
integrator system, highlighting the reliability of the DR-PRS w.r.t. the
Wasserstein set and performance of the resulting SMPC.Comment: Extended version with proofs; accepted for presentation at the 21st
IFAC World Congress 202
Multi-Hypothesis Interactions in Game-Theoretic Motion Planning
We present a novel method for handling uncertainty about the intentions of
non-ego players in dynamic games, with application to motion planning for
autonomous vehicles. Equilibria in these games explicitly account for
interaction among other agents in the environment, such as drivers and
pedestrians. Our method models the uncertainty about the intention of other
agents by constructing multiple hypotheses about the objectives and constraints
of other agents in the scene. For each candidate hypothesis, we associate a
Bernoulli random variable representing the probability of that hypothesis,
which may or may not be independent of the probability of other hypotheses. We
leverage constraint asymmetries and feedback information patterns to
incorporate the probabilities of hypotheses in a natural way. Specifically,
increasing the probability associated with a given hypothesis from to
shifts the responsibility of collision avoidance from the hypothesized agent to
the ego agent. This method allows the generation of interactive trajectories
for the ego agent, where the level of assertiveness or caution that the ego
exhibits is directly related to the easy-to-model uncertainty it maintains
about the scene.Comment: For associated mp4 file, see https://youtu.be/x7VtYDrWTW
Consistency of Distributionally Robust Risk-and Chance-Constrained Optimization under Wasserstein Ambiguity Sets
We study stochastic optimization problems with chance and risk constraints, where in the latter, risk is quantified in terms of the conditional value-at-risk (CVaR). We consider the distributionally robust versions of these problems, where the constraints are required to hold for a family of distributions constructed from the observed realizations of the uncertainty via the Wasserstein distance. Our main results establish that if the samples are drawn independently from an underlying distribution and the problems satisfy suitable technical assumptions, then the optimal value and optimizers of the distributionally robust versions of these problems converge to the respective quantities of the original problems, as the sample size increases
Safe Zero-Shot Model-Based Learning and Control: A Wasserstein Distributionally Robust Approach
This paper explores distributionally robust zero-shot model-based learning
and control using Wasserstein ambiguity sets. Conventional model-based
reinforcement learning algorithms struggle to guarantee feasibility throughout
the online learning process. We address this open challenge with the following
approach. Using a stochastic model-predictive control (MPC) strategy, we
augment safety constraints with affine random variables corresponding to the
instantaneous empirical distributions of modeling error. We obtain these
distributions by evaluating model residuals in real time throughout the online
learning process. By optimizing over the worst case modeling error distribution
defined within a Wasserstein ambiguity set centered about our empirical
distributions, we can approach the nominal constraint boundary in a provably
safe way. We validate the performance of our approach using a case study of
lithium-ion battery fast charging, a relevant and safety-critical energy
systems control application. Our results demonstrate marked improvements in
safety compared to a basic learning model-predictive controller, with
constraints satisfied at every instance during online learning and control.Comment: In review for CDC2