1,240 research outputs found
ALGAMES: A Fast Solver for Constrained Dynamic Games
Dynamic games are an effective paradigm for dealing with the control of
multiple interacting actors. This paper introduces ALGAMES (Augmented
Lagrangian GAME-theoretic Solver), a solver that handles trajectory
optimization problems with multiple actors and general nonlinear state and
input constraints. Its novelty resides in satisfying the first order optimality
conditions with a quasi-Newton root-finding algorithm and rigorously enforcing
constraints using an augmented Lagrangian formulation. We evaluate our solver
in the context of autonomous driving on scenarios with a strong level of
interactions between the vehicles. We assess the robustness of the solver using
Monte Carlo simulations. It is able to reliably solve complex problems like
ramp merging with three vehicles three times faster than a state-of-the-art
DDP-based approach. A model predictive control (MPC) implementation of the
algorithm demonstrates real-time performance on complex autonomous driving
scenarios with an update frequency higher than 60 Hz.Comment: 10 pages, 8 figures, submitted to Robotics: Science and Systems
Conference (RSS) 202
BM3D Frames and Variational Image Deblurring
A family of the Block Matching 3-D (BM3D) algorithms for various imaging
problems has been recently proposed within the framework of nonlocal patch-wise
image modeling [1], [2]. In this paper we construct analysis and synthesis
frames, formalizing the BM3D image modeling and use these frames to develop
novel iterative deblurring algorithms. We consider two different formulations
of the deblurring problem: one given by minimization of the single objective
function and another based on the Nash equilibrium balance of two objective
functions. The latter results in an algorithm where the denoising and
deblurring operations are decoupled. The convergence of the developed
algorithms is proved. Simulation experiments show that the decoupled algorithm
derived from the Nash equilibrium formulation demonstrates the best numerical
and visual results and shows superiority with respect to the state of the art
in the field, confirming a valuable potential of BM3D-frames as an advanced
image modeling tool.Comment: Submitted to IEEE Transactions on Image Processing on May 18, 2011.
implementation of the proposed algorithm is available as part of the BM3D
package at http://www.cs.tut.fi/~foi/GCF-BM3
Randomized Lagrangian Stochastic Approximation for Large-Scale Constrained Stochastic Nash Games
In this paper, we consider stochastic monotone Nash games where each player's
strategy set is characterized by possibly a large number of explicit convex
constraint inequalities. Notably, the functional constraints of each player may
depend on the strategies of other players, allowing for capturing a subclass of
generalized Nash equilibrium problems (GNEP). While there is limited work that
provide guarantees for this class of stochastic GNEPs, even when the functional
constraints of the players are independent of each other, the majority of the
existing methods rely on employing projected stochastic approximation (SA)
methods. However, the projected SA methods perform poorly when the constraint
set is afflicted by the presence of a large number of possibly nonlinear
functional inequalities. Motivated by the absence of performance guarantees for
computing the Nash equilibrium in constrained stochastic monotone Nash games,
we develop a single timescale randomized Lagrangian multiplier stochastic
approximation method where in the primal space, we employ an SA scheme, and in
the dual space, we employ a randomized block-coordinate scheme where only a
randomly selected Lagrangian multiplier is updated. We show that our method
achieves a convergence rate of
for suitably defined
suboptimality and infeasibility metrics in a mean sense.Comment: The result of this paper has been presented at International
Conference on Continuous Optimization (ICCOPT) 2022 and East Coast
Optimization Meeting (ECOM) 202
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