Shubhankar Agarwal

Junette Hsin, Shubhankar Agarwal, Adam Thorpe et al.

In this paper, we address the challenge of deriving dynamical models from sparse and noisy data. High-quality data is crucial for symbolic regression algorithms; limited and noisy data can present modeling challenges. To overcome this, we combine Gaussian process regression with a sparse identification of nonlinear dynamics (SINDy) method to denoise the data and identify nonlinear dynamical equations. Our approach GPSINDy offers improved robustness with sparse, noisy data compared to SINDy alone. We demonstrate its effectiveness on simulation data from Lotka-Volterra and unicycle models and hardware data from an NVIDIA JetRacer system. We show superior performance over baselines including more than 50% improvement over SINDy and other baselines in predicting future trajectories from noise-corrupted and sparse 5 Hz data.

Shubhankar Agarwal, David Fridovich-Keil, Sandeep P. Chinchali

Modern robots require accurate forecasts to make optimal decisions in the real world. For example, self-driving cars need an accurate forecast of other agents' future actions to plan safe trajectories. Current methods rely heavily on historical time series to accurately predict the future. However, relying entirely on the observed history is problematic since it could be corrupted by noise, have outliers, or not completely represent all possible outcomes. To solve this problem, we propose a novel framework for generating robust forecasts for robotic control. In order to model real-world factors affecting future forecasts, we introduce the notion of an adversary, which perturbs observed historical time series to increase a robot's ultimate control cost. Specifically, we model this interaction as a zero-sum two-player game between a robot's forecaster and this hypothetical adversary. We show that our proposed game may be solved to a local Nash equilibrium using gradient-based optimization techniques. Furthermore, we show that a forecaster trained with our method performs 30.14% better on out-of-distribution real-world lane change data than baselines.

Oguzhan Akcin, Po-han Li, Shubhankar Agarwal et al.

Fleets of networked autonomous vehicles (AVs) collect terabytes of sensory data, which is often transmitted to central servers (the ''cloud'') for training machine learning (ML) models. Ideally, these fleets should upload all their data, especially from rare operating contexts, in order to train robust ML models. However, this is infeasible due to prohibitive network bandwidth and data labeling costs. Instead, we propose a cooperative data sampling strategy where geo-distributed AVs collaborate to collect a diverse ML training dataset in the cloud. Since the AVs have a shared objective but minimal information about each other's local data distribution and perception model, we can naturally cast cooperative data collection as an $N$-player mathematical game. We show that our cooperative sampling strategy uses minimal information to converge to a centralized oracle policy with complete information about all AVs. Moreover, we theoretically characterize the performance benefits of our game-theoretic strategy compared to greedy sampling. Finally, we experimentally demonstrate that our method outperforms standard benchmarks by up to $21.9\%$ on 4 perception datasets, including for autonomous driving in adverse weather conditions. Crucially, our experimental results on real-world datasets closely align with our theoretical guarantees.

Sai Shankar Narasimhan, Shubhankar Agarwal, Oguzhan Akcin et al.

Imagine generating a city's electricity demand pattern based on weather, the presence of an electric vehicle, and location, which could be used for capacity planning during a winter freeze. Such real-world time series are often enriched with paired heterogeneous contextual metadata (e.g., weather and location). Current approaches to time series generation often ignore this paired metadata. Additionally, the heterogeneity in metadata poses several practical challenges in adapting existing conditional generation approaches from the image, audio, and video domains to the time series domain. To address this gap, we introduce TIME WEAVER, a novel diffusion-based model that leverages the heterogeneous metadata in the form of categorical, continuous, and even time-variant variables to significantly improve time series generation. Additionally, we show that naive extensions of standard evaluation metrics from the image to the time series domain are insufficient. These metrics do not penalize conditional generation approaches for their poor specificity in reproducing the metadata-specific features in the generated time series. Thus, we innovate a novel evaluation metric that accurately captures the specificity of conditional generation and the realism of the generated time series. We show that TIME WEAVER outperforms state-of-the-art benchmarks, such as Generative Adversarial Networks (GANs), by up to 30% in downstream classification tasks on real-world energy, medical, air quality, and traffic datasets.

Sai Shankar Narasimhan, Shubhankar Agarwal, Litu Rout et al.

Generating realistic time series samples is crucial for stress-testing models and protecting user privacy by using synthetic data. In engineering and safety-critical applications, these samples must meet certain hard constraints that are domain-specific or naturally imposed by physics or nature. Consider, for example, generating electricity demand patterns with constraints on peak demand times. This can be used to stress-test the functioning of power grids during adverse weather conditions. Existing approaches for generating constrained time series are either not scalable or degrade sample quality. To address these challenges, we introduce Constrained Posterior Sampling (CPS), a diffusion-based sampling algorithm that aims to project the posterior mean estimate into the constraint set after each denoising update. Notably, CPS scales to a large number of constraints ($\sim100$) without requiring additional training. We provide theoretical justifications highlighting the impact of our projection step on sampling. Empirically, CPS outperforms state-of-the-art methods in sample quality and similarity to real time series by around 70\% and 22\%, respectively, on real-world stocks, traffic, and air quality datasets.

Shubhankar Agarwal, Hamzah I. Khan, Sandeep P. Chinchali et al.

Saddle point optimization is a critical problem employed in numerous real-world applications, including portfolio optimization, generative adversarial networks, and robotics. It has been extensively studied in cases where the objective function is known and differentiable. Existing work in black-box settings with unknown objectives that can only be sampled either assumes convexity-concavity in the objective to simplify the problem or operates with noisy gradient estimators. In contrast, we introduce a framework inspired by Bayesian optimization which utilizes Gaussian processes to model the unknown (potentially nonconvex-nonconcave) objective and requires only zeroth-order samples. Our approach frames the saddle point optimization problem as a two-level process which can flexibly integrate existing and novel approaches to this problem. The upper level of our framework produces a model of the objective function by sampling in promising locations, and the lower level of our framework uses the existing model to frame and solve a general-sum game to identify locations to sample. This lower level procedure can be designed in complementary ways, and we demonstrate the flexibility of our approach by introducing variants which appropriately trade off between factors like runtime, the cost of function evaluations, and the number of available initial samples. We experimentally demonstrate these algorithms on synthetic and realistic datasets in black-box nonconvex-nonconcave settings, showcasing their ability to efficiently locate local saddle points in these contexts.

Sameep Chattopadhyay, Pulkit Paliwal, Sai Shankar Narasimhan et al.

Time series forecasts are often influenced by exogenous contextual features in addition to their corresponding history. For example, in financial settings, it is hard to accurately predict a stock price without considering public sentiments and policy decisions in the form of news articles, tweets, etc. Though this is common knowledge, the current state-of-the-art (SOTA) forecasting models fail to incorporate such contextual information, owing to its heterogeneity and multimodal nature. To address this, we introduce ContextFormer, a novel plug-and-play method to surgically integrate multimodal contextual information into existing pre-trained forecasting models. ContextFormer effectively distills forecast-specific information from rich multimodal contexts, including categorical, continuous, time-varying, and even textual information, to significantly enhance the performance of existing base forecasters. ContextFormer outperforms SOTA forecasting models by up to 30% on a range of real-world datasets spanning energy, traffic, environmental, and financial domains.

Shubhankar Agarwal, Harshit Sikchi, Cole Gulino et al.

A popular way to plan trajectories in dynamic urban scenarios for Autonomous Vehicles is to rely on explicitly specified and hand crafted cost functions, coupled with random sampling in the trajectory space to find the minimum cost trajectory. Such methods require a high number of samples to find a low-cost trajectory and might end up with a highly suboptimal trajectory given the planning time budget. We explore the application of normalizing flows for improving the performance of trajectory planning for autonomous vehicles (AVs). Our key insight is to learn a sampling policy in a low-dimensional latent space of expert-like trajectories, out of which the best sample is selected for execution. By modeling the trajectory planner's cost manifold as an energy function, we learn a scene conditioned mapping from the prior to a Boltzmann distribution over the AV control space. Finally, we demonstrate the effectiveness of our approach on real-world datasets over IL and hand-constructed trajectory sampling techniques.