8,832 research outputs found
Data based identification and prediction of nonlinear and complex dynamical systems
We thank Dr. R. Yang (formerly at ASU), Dr. R.-Q. Su (formerly at ASU), and Mr. Zhesi Shen for their contributions to a number of original papers on which this Review is partly based. This work was supported by ARO under Grant No. W911NF-14-1-0504. W.-X. Wang was also supported by NSFC under Grants No. 61573064 and No. 61074116, as well as by the Fundamental Research Funds for the Central Universities, Beijing Nova Programme.Peer reviewedPostprin
On a Connection between Differential Games, Optimal Control, and Energy-based Models for Multi-Agent Interactions
Game theory offers an interpretable mathematical framework for modeling
multi-agent interactions. However, its applicability in real-world robotics
applications is hindered by several challenges, such as unknown agents'
preferences and goals. To address these challenges, we show a connection
between differential games, optimal control, and energy-based models and
demonstrate how existing approaches can be unified under our proposed
Energy-based Potential Game formulation. Building upon this formulation, this
work introduces a new end-to-end learning application that combines neural
networks for game-parameter inference with a differentiable game-theoretic
optimization layer, acting as an inductive bias. The experiments using
simulated mobile robot pedestrian interactions and real-world automated driving
data provide empirical evidence that the game-theoretic layer improves the
predictive performance of various neural network backbones.Comment: International Conference on Machine Learning, Workshop on New
Frontiers in Learning, Control, and Dynamical Systems (ICML 2023
Frontiers4LCD
DockGame: Cooperative Games for Multimeric Rigid Protein Docking
Protein interactions and assembly formation are fundamental to most
biological processes. Predicting the assembly structure from constituent
proteins -- referred to as the protein docking task -- is thus a crucial step
in protein design applications. Most traditional and deep learning methods for
docking have focused mainly on binary docking, following either a search-based,
regression-based, or generative modeling paradigm. In this paper, we focus on
the less-studied multimeric (i.e., two or more proteins) docking problem. We
introduce DockGame, a novel game-theoretic framework for docking -- we view
protein docking as a cooperative game between proteins, where the final
assembly structure(s) constitute stable equilibria w.r.t. the underlying game
potential. Since we do not have access to the true potential, we consider two
approaches - i) learning a surrogate game potential guided by physics-based
energy functions and computing equilibria by simultaneous gradient updates, and
ii) sampling from the Gibbs distribution of the true potential by learning a
diffusion generative model over the action spaces (rotations and translations)
of all proteins. Empirically, on the Docking Benchmark 5.5 (DB5.5) dataset,
DockGame has much faster runtimes than traditional docking methods, can
generate multiple plausible assembly structures, and achieves comparable
performance to existing binary docking baselines, despite solving the harder
task of coordinating multiple protein chains.Comment: Under Revie
Universal Scalable Robust Solvers from Computational Information Games and fast eigenspace adapted Multiresolution Analysis
We show how the discovery of robust scalable numerical solvers for arbitrary
bounded linear operators can be automated as a Game Theory problem by
reformulating the process of computing with partial information and limited
resources as that of playing underlying hierarchies of adversarial information
games. When the solution space is a Banach space endowed with a quadratic
norm , the optimal measure (mixed strategy) for such games (e.g. the
adversarial recovery of , given partial measurements with
, using relative error in -norm as a loss) is a
centered Gaussian field solely determined by the norm , whose
conditioning (on measurements) produces optimal bets. When measurements are
hierarchical, the process of conditioning this Gaussian field produces a
hierarchy of elementary bets (gamblets). These gamblets generalize the notion
of Wavelets and Wannier functions in the sense that they are adapted to the
norm and induce a multi-resolution decomposition of that is
adapted to the eigensubspaces of the operator defining the norm .
When the operator is localized, we show that the resulting gamblets are
localized both in space and frequency and introduce the Fast Gamblet Transform
(FGT) with rigorous accuracy and (near-linear) complexity estimates. As the FFT
can be used to solve and diagonalize arbitrary PDEs with constant coefficients,
the FGT can be used to decompose a wide range of continuous linear operators
(including arbitrary continuous linear bijections from to or
to ) into a sequence of independent linear systems with uniformly bounded
condition numbers and leads to
solvers and eigenspace adapted Multiresolution Analysis (resulting in near
linear complexity approximation of all eigensubspaces).Comment: 142 pages. 14 Figures. Presented at AFOSR (Aug 2016), DARPA (Sep
2016), IPAM (Apr 3, 2017), Hausdorff (April 13, 2017) and ICERM (June 5,
2017
Optimal Data Acquisition for Statistical Estimation
We consider a data analyst's problem of purchasing data from strategic agents
to compute an unbiased estimate of a statistic of interest. Agents incur
private costs to reveal their data and the costs can be arbitrarily correlated
with their data. Once revealed, data are verifiable. This paper focuses on
linear unbiased estimators. We design an individually rational and incentive
compatible mechanism that optimizes the worst-case mean-squared error of the
estimation, where the worst-case is over the unknown correlation between costs
and data, subject to a budget constraint in expectation. We characterize the
form of the optimal mechanism in closed-form. We further extend our results to
acquiring data for estimating a parameter in regression analysis, where private
costs can correlate with the values of the dependent variable but not with the
values of the independent variables
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