arXiv subjects

Kamyar Azizzadenesheli

Publications and source records attributed to Kamyar Azizzadenesheli.

At least 73 records · Page 4Linked to original sources

arXiv2022

Off-Policy Risk Assessment in Markov Decision Processes

Addressing such diverse ends as safety alignment with human preferences, and the efficiency of learning, a growing line of reinforcement learning research focuses on risk functionals that depend on the entire distribution of returns. Recent work on \emph{off-policy risk assessment} (OPRA) for contextual bandits introduced consistent estimators for the target policy's CDF of returns along with finite sample guarantees that extend to (and hold simultaneously over) all risk. In this paper, we lift OPRA to Markov decision processes (MDPs), where importance sampling (IS) CDF estimators suffer high variance on longer trajectories due to small effective sample size. To mitigate these problems, we incorporate model-based estimation to develop the first doubly robust (DR) estimator for the CDF of returns in MDPs. This estimator enjoys significantly less variance and, when the model is well specified, achieves the Cramer-Rao variance lower bound. Moreover, for many risk functionals, the downstream estimates enjoy both lower bias and lower variance. Additionally, we derive the first minimax lower bounds for off-policy CDF and risk estimation, which match our error bounds up to a constant factor. Finally, we demonstrate the precision of our DR CDF estimates experimentally on several different environments.

cs.LG↗

arXiv2022

HypoSVI: Hypocenter inversion with Stein variational inference and Physics Informed Neural Networks

We introduce a scheme for probabilistic hypocenter inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation. This allows for rapid approximation of the posterior by iteratively optimizing a collection of particles against a kernelized Stein discrepancy. We show that the method is well-equipped to handle highly multimodal posterior distributions, which are common in hypocentral inverse problems. A suite of experiments is performed to examine the influence of the various hyperparameters. Once trained, the method is valid for any seismic network geometry within the study area without the need to build travel time tables. We show that the computational demands scale efficiently with the number of differential times, making it ideal for large-N sensing technologies like Distributed Acoustic Sensing. The techniques outlined in this manuscript have considerable implications beyond just ray-tracing procedures, with the work flow applicable to other fields with computationally expensive inversion procedures such as full waveform inversion.

physics.geo-ph↗

arXiv2022

Compactly Restrictable Metric Policy Optimization Problems

We study policy optimization problems for deterministic Markov decision processes (MDPs) with metric state and action spaces, which we refer to as Metric Policy Optimization Problems (MPOPs). Our goal is to establish theoretical results on the well-posedness of MPOPs that can characterize practically relevant continuous control systems. To do so, we define a special class of MPOPs called Compactly Restrictable MPOPs (CR-MPOPs), which are flexible enough to capture the complex behavior of robotic systems but specific enough to admit solutions using dynamic programming methods such as value iteration. We show how to arrive at CR-MPOPs using forward-invariance. We further show that our theoretical results on CR-MPOPs can be used to characterize feedback linearizable control affine systems.

math.OC↗

arXiv2022

Supervised Learning with General Risk Functionals

Standard uniform convergence results bound the generalization gap of the expected loss over a hypothesis class. The emergence of risk-sensitive learning requires generalization guarantees for functionals of the loss distribution beyond the expectation. While prior works specialize in uniform convergence of particular functionals, our work provides uniform convergence for a general class of Hölder risk functionals for which the closeness in the Cumulative Distribution Function (CDF) entails closeness in risk. We establish the first uniform convergence results for estimating the CDF of the loss distribution, yielding guarantees that hold simultaneously both over all Hölder risk functionals and over all hypotheses. Thus licensed to perform empirical risk minimization, we develop practical gradient-based methods for minimizing distortion risks (widely studied subset of Hölder risks that subsumes the spectral risks, including the mean, conditional value at risk, cumulative prospect theory risks, and others) and provide convergence guarantees. In experiments, we demonstrate the efficacy of our learning procedure, both in settings where uniform convergence results hold and in high-dimensional settings with deep networks.

stat.ML↗

arXiv2022

Langevin Monte Carlo for Contextual Bandits

We study the efficiency of Thompson sampling for contextual bandits. Existing Thompson sampling-based algorithms need to construct a Laplace approximation (i.e., a Gaussian distribution) of the posterior distribution, which is inefficient to sample in high dimensional applications for general covariance matrices. Moreover, the Gaussian approximation may not be a good surrogate for the posterior distribution for general reward generating functions. We propose an efficient posterior sampling algorithm, viz., Langevin Monte Carlo Thompson Sampling (LMC-TS), that uses Markov Chain Monte Carlo (MCMC) methods to directly sample from the posterior distribution in contextual bandits. Our method is computationally efficient since it only needs to perform noisy gradient descent updates without constructing the Laplace approximation of the posterior distribution. We prove that the proposed algorithm achieves the same sublinear regret bound as the best Thompson sampling algorithms for a special case of contextual bandits, viz., linear contextual bandits. We conduct experiments on both synthetic data and real-world datasets on different contextual bandit models, which demonstrates that directly sampling from the posterior is both computationally efficient and competitive in performance.

cs.LG↗

arXiv2022

Thompson Sampling Achieves $\tilde O(\sqrt{T})$ Regret in Linear Quadratic Control

Thompson Sampling (TS) is an efficient method for decision-making under uncertainty, where an action is sampled from a carefully prescribed distribution which is updated based on the observed data. In this work, we study the problem of adaptive control of stabilizable linear-quadratic regulators (LQRs) using TS, where the system dynamics are unknown. Previous works have established that $\tilde O(\sqrt{T})$ frequentist regret is optimal for the adaptive control of LQRs. However, the existing methods either work only in restrictive settings, require a priori known stabilizing controllers, or utilize computationally intractable approaches. We propose an efficient TS algorithm for the adaptive control of LQRs, TS-based Adaptive Control, TSAC, that attains $\tilde O(\sqrt{T})$ regret, even for multidimensional systems, thereby solving the open problem posed in Abeille and Lazaric (2018). TSAC does not require a priori known stabilizing controller and achieves fast stabilization of the underlying system by effectively exploring the environment in the early stages. Our result hinges on developing a novel lower bound on the probability that the TS provides an optimistic sample. By carefully prescribing an early exploration strategy and a policy update rule, we show that TS achieves order-optimal regret in adaptive control of multidimensional stabilizable LQRs. We empirically demonstrate the performance and the efficiency of TSAC in several adaptive control tasks.

cs.LG↗

arXiv2022

Reinforcement Learning with Fast Stabilization in Linear Dynamical Systems

In this work, we study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems. When learning a dynamical system, one needs to stabilize the unknown dynamics in order to avoid system blow-ups. We propose an algorithm that certifies fast stabilization of the underlying system by effectively exploring the environment with an improved exploration strategy. We show that the proposed algorithm attains $\tilde{\mathcal{O}}(\sqrt{T})$ regret after $T$ time steps of agent-environment interaction. We also show that the regret of the proposed algorithm has only a polynomial dependence in the problem dimensions, which gives an exponential improvement over the prior methods. Our improved exploration method is simple, yet efficient, and it combines a sophisticated exploration policy in RL with an isotropic exploration strategy to achieve fast stabilization and improved regret. We empirically demonstrate that the proposed algorithm outperforms other popular methods in several adaptive control tasks.

cs.LG↗

arXiv2022

KCRL: Krasovskii-Constrained Reinforcement Learning with Guaranteed Stability in Nonlinear Dynamical Systems

Learning a dynamical system requires stabilizing the unknown dynamics to avoid state blow-ups. However, current reinforcement learning (RL) methods lack stabilization guarantees, which limits their applicability for the control of safety-critical systems. We propose a model-based RL framework with formal stability guarantees, Krasovskii Constrained RL (KCRL), that adopts Krasovskii's family of Lyapunov functions as a stability constraint. The proposed method learns the system dynamics up to a confidence interval using feature representation, e.g. Random Fourier Features. It then solves a constrained policy optimization problem with a stability constraint based on Krasovskii's method using a primal-dual approach to recover a stabilizing policy. We show that KCRL is guaranteed to learn a stabilizing policy in a finite number of interactions with the underlying unknown system. We also derive the sample complexity upper bound for stabilization of unknown nonlinear dynamical systems via the KCRL framework.

cs.LG↗

arXiv2022

Competitive Gradient Optimization

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO ), a gradient-based method that incorporates the interactions between the two players in zero-sum games for optimization updates. We provide continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, CGO predecessors degenerate to their gradient descent ascent (GDA) variants. We provide a rate of convergence to stationary points and further propose a generalized class of $α$-coherent function for which we provide convergence analysis. We show that for strictly $α$-coherent functions, our algorithm convergences to a saddle point. Moreover, we propose optimistic CGO (OCGO), an optimistic variant, for which we show convergence rate to saddle points in $α$-coherent class of functions.

math.OC↗

arXiv2022

U-FNO -- An enhanced Fourier neural operator-based deep-learning model for multiphase flow

Numerical simulation of multiphase flow in porous media is essential for many geoscience applications. Machine learning models trained with numerical simulation data can provide a faster alternative to traditional simulators. Here we present U-FNO, a novel neural network architecture for solving multiphase flow problems with superior accuracy, speed, and data efficiency. U-FNO is designed based on the newly proposed Fourier neural operator (FNO), which has shown excellent performance in single-phase flows. We extend the FNO-based architecture to a highly complex CO2-water multiphase problem with wide ranges of permeability and porosity heterogeneity, anisotropy, reservoir conditions, injection configurations, flow rates, and multiphase flow properties. The U-FNO architecture is more accurate in gas saturation and pressure buildup predictions than the original FNO and a state-of-the-art convolutional neural network (CNN) benchmark. Meanwhile, it has superior data utilization efficiency, requiring only a third of the training data to achieve the equivalent accuracy as CNN. U-FNO provides superior performance in highly heterogeneous geological formations and critically important applications such as gas saturation and pressure buildup "fronts" determination. The trained model can serve as a general-purpose alternative to routine numerical simulations of 2D-radial CO2 injection problems with significant speed-ups than traditional simulators.

physics.geo-ph↗

arXiv2022

FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators

FourCastNet, short for Fourier Forecasting Neural Network, is a global data-driven weather forecasting model that provides accurate short to medium-range global predictions at $0.25^{\circ}$ resolution. FourCastNet accurately forecasts high-resolution, fast-timescale variables such as the surface wind speed, precipitation, and atmospheric water vapor. It has important implications for planning wind energy resources, predicting extreme weather events such as tropical cyclones, extra-tropical cyclones, and atmospheric rivers. FourCastNet matches the forecasting accuracy of the ECMWF Integrated Forecasting System (IFS), a state-of-the-art Numerical Weather Prediction (NWP) model, at short lead times for large-scale variables, while outperforming IFS for variables with complex fine-scale structure, including precipitation. FourCastNet generates a week-long forecast in less than 2 seconds, orders of magnitude faster than IFS. The speed of FourCastNet enables the creation of rapid and inexpensive large-ensemble forecasts with thousands of ensemble-members for improving probabilistic forecasting. We discuss how data-driven deep learning models such as FourCastNet are a valuable addition to the meteorology toolkit to aid and augment NWP models.

physics.ao-ph↗

arXiv2022

Joint Stabilization and Regret Minimization through Switching in Over-Actuated Systems (extended version)

Adaptively controlling and minimizing regret in unknown dynamical systems while controlling the growth of the system state is crucial in real-world applications. In this work, we study the problem of stabilization and regret minimization of linear over-actuated dynamical systems. We propose an optimism-based algorithm that leverages possibility of switching between actuating modes in order to alleviate state explosion during initial time steps. We theoretically study the rate at which our algorithm learns a stabilizing controller and prove that it achieves a regret upper bound of $\mathcal{O}(\sqrt{T})$.

eess.SY↗

arXiv2021

Meta-Adaptive Nonlinear Control: Theory and Algorithms

We present an online multi-task learning approach for adaptive nonlinear control, which we call Online Meta-Adaptive Control (OMAC). The goal is to control a nonlinear system subject to adversarial disturbance and unknown $\textit{environment-dependent}$ nonlinear dynamics, under the assumption that the environment-dependent dynamics can be well captured with some shared representation. Our approach is motivated by robot control, where a robotic system encounters a sequence of new environmental conditions that it must quickly adapt to. A key emphasis is to integrate online representation learning with established methods from control theory, in order to arrive at a unified framework that yields both control-theoretic and learning-theoretic guarantees. We provide instantiations of our approach under varying conditions, leading to the first non-asymptotic end-to-end convergence guarantee for multi-task nonlinear control. OMAC can also be integrated with deep representation learning. Experiments show that OMAC significantly outperforms conventional adaptive control approaches which do not learn the shared representation, in inverted pendulum and 6-DoF drone control tasks under varying wind conditions.

cs.LG↗

arXiv2021

Seismic wave propagation and inversion with Neural Operators

Seismic wave propagation forms the basis for most aspects of seismological research, yet solving the wave equation is a major computational burden that inhibits the progress of research. This is exacerbated by the fact that new simulations must be performed when the velocity structure or source location is perturbed. Here, we explore a prototype framework for learning general solutions using a recently developed machine learning paradigm called Neural Operator. A trained Neural Operator can compute a solution in negligible time for any velocity structure or source location. We develop a scheme to train Neural Operators on an ensemble of simulations performed with random velocity models and source locations. As Neural Operators are grid-free, it is possible to evaluate solutions on higher resolution velocity models than trained on, providing additional computational efficiency. We illustrate the method with the 2D acoustic wave equation and demonstrate the method's applicability to seismic tomography, using reverse mode automatic differentiation to compute gradients of the wavefield with respect to the velocity structure. The developed procedure is nearly an order of magnitude faster than using conventional numerical methods for full waveform inversion.

physics.geo-ph↗

arXiv2021

Finite-time System Identification and Adaptive Control in Autoregressive Exogenous Systems

Autoregressive exogenous (ARX) systems are the general class of input-output dynamical systems used for modeling stochastic linear dynamical systems (LDS) including partially observable LDS such as LQG systems. In this work, we study the problem of system identification and adaptive control of unknown ARX systems. We provide finite-time learning guarantees for the ARX systems under both open-loop and closed-loop data collection. Using these guarantees, we design adaptive control algorithms for unknown ARX systems with arbitrary strongly convex or convex quadratic regulating costs. Under strongly convex cost functions, we design an adaptive control algorithm based on online gradient descent to design and update the controllers that are constructed via a convex controller reparametrization. We show that our algorithm has $\tilde{\mathcal{O}}(\sqrt{T})$ regret via explore and commit approach and if the model estimates are updated in epochs using closed-loop data collection, it attains the optimal regret of $\text{polylog}(T)$ after $T$ time-steps of interaction. For the case of convex quadratic cost functions, we propose an adaptive control algorithm that deploys the optimism in the face of uncertainty principle to design the controller. In this setting, we show that the explore and commit approach has a regret upper bound of $\tilde{\mathcal{O}}(T^{2/3})$, and the adaptive control with continuous model estimate updates attains $\tilde{\mathcal{O}}(\sqrt{T})$ regret after $T$ time-steps.

cs.LG↗

arXiv2021

Off-Policy Risk Assessment in Contextual Bandits

Even when unable to run experiments, practitioners can evaluate prospective policies, using previously logged data. However, while the bandits literature has adopted a diverse set of objectives, most research on off-policy evaluation to date focuses on the expected reward. In this paper, we introduce Lipschitz risk functionals, a broad class of objectives that subsumes conditional value-at-risk (CVaR), variance, mean-variance, many distorted risks, and CPT risks, among others. We propose Off-Policy Risk Assessment (OPRA), a framework that first estimates a target policy's CDF and then generates plugin estimates for any collection of Lipschitz risks, providing finite sample guarantees that hold simultaneously over the entire class. We instantiate OPRA with both importance sampling and doubly robust estimators. Our primary theoretical contributions are (i) the first uniform concentration inequalities for both CDF estimators in contextual bandits and (ii) error bounds on our Lipschitz risk estimates, which all converge at a rate of $O(1/\sqrt{n})$.

cs.LG↗

arXiv2021

Importance Weight Estimation and Generalization in Domain Adaptation under Label Shift

We study generalization under labeled shift for categorical and general normed label spaces. We propose a series of methods to estimate the importance weights from labeled source to unlabeled target domain and provide confidence bounds for these estimators. We deploy these estimators and provide generalization bounds in the unlabeled target domain.

cs.LG↗

arXiv2021

Fourier Neural Operator for Parametric Partial Differential Equations

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

cs.LG↗