Deepan Muthirayan

Deepan Muthirayan, Pramod P. Khargonekar

In this paper, we propose a novel control architecture, inspired from neuroscience, for adaptive control of continuous-time systems. The proposed architecture, in the setting of standard Neural Network (NN) based adaptive control, augments an external working memory to the NN. The controller, through a write operation, writes the hidden layer feature vector of the NN to the external working memory and can also update this information with the observed error in the output. Through a read operation, the controller retrieves information from the working memory to modify the final control signal. First, we consider a simpler estimation problem to theoretically study the effect of an external memory and prove that the estimation accuracy can be improved by incorporating memory. We then consider a model reference NN adaptive controller for linear systems with matched uncertainty to implement and illustrate our ideas. We prove that the resulting controller leads to a Uniformly Bounded (UB) stable closed loop system. Through extensive simulations and specific metrics, such as peak deviation and settling time, we show that memory augmentation improves learning significantly. Importantly, we also provide evidence for and insights on the mechanism by which this specific memory augmentation improves learning.

Deepan Muthirayan, Dileep Kalathil, Pramod P. Khargonekar

In this paper, we consider the problem of finding a meta-learning online control algorithm that can learn across the tasks when faced with a sequence of $N$ (similar) control tasks. Each task involves controlling a linear dynamical system for a finite horizon of $T$ time steps. The cost function and system noise at each time step are adversarial and unknown to the controller before taking the control action. Meta-learning is a broad approach where the goal is to prescribe an online policy for any new unseen task exploiting the information from other tasks and the similarity between the tasks. We propose a meta-learning online control algorithm for the control setting and characterize its performance by \textit{meta-regret}, the average cumulative regret across the tasks. We show that when the number of tasks are sufficiently large, our proposed approach achieves a meta-regret that is smaller by a factor $D/D^{*}$ compared to an independent-learning online control algorithm which does not perform learning across the tasks, where $D$ is a problem constant and $D^{*}$ is a scalar that decreases with increase in the similarity between tasks. Thus, when the sequence of tasks are similar the regret of the proposed meta-learning online control is significantly lower than that of the naive approaches without meta-learning. We also present experiment results to demonstrate the superior performance achieved by our meta-learning algorithm.

Deepan Muthirayan, Jianjun Yuan, Pramod P. Khargonekar

In this paper, we investigate the framework of Online Convex Optimization (OCO) for online learning. OCO offers a very powerful online learning framework for many applications. In this context, we study a specific framework of OCO called {\it OCO with long term constraints}. Long term constraints are introduced typically as an alternative to reduce the complexity of the projection at every update step in online optimization. While many algorithmic advances have been made towards online optimization with long term constraints, these algorithms typically assume that the sequence of cost functions over a certain $T$ finite steps that determine the cost to the online learner are adversarially generated. In many circumstances, the sequence of cost functions may not be unrelated, and thus predictable from those observed till a point of time. In this paper, we study the setting where the sequences are predictable. We present a novel online optimization algorithm for online optimization with long term constraints that can leverage such predictability. We show that, with a predictor that can supply the gradient information of the next function in the sequence, our algorithm can achieve an overall regret and constraint violation rate that is strictly less than the rate that is achievable without prediction.

Deepan Muthirayan, Chinmay Maheshwari, Pramod P. Khargonekar et al.

We study the problem of online learning in two-sided non-stationary matching markets, where the objective is to converge to a stable match. In particular, we consider the setting where one side of the market, the arms, has fixed known set of preferences over the other side, the players. While this problem has been studied when the players have fixed but unknown preferences, in this work we study the problem of how to learn when the preferences of the players are time varying and unknown. Our contribution is a methodology that can handle any type of preference structure and variation scenario. We show that, with the proposed algorithm, each player receives a uniform sub-linear regret of {$\widetilde{\mathcal{O}}(L^{1/2}_TT^{1/2})$} up to the number of changes in the underlying preferences of the agents, $L_T$. Therefore, we show that the optimal rates for single-agent learning can be achieved in spite of the competition up to a difference of a constant factor. We also discuss extensions of this algorithm to the case where the number of changes need not be known a priori.

Deepan Muthirayan, Pramod P. Khargonekar

In this paper, we consider the problem of learning online to manage Demand Response (DR) resources. A typical DR mechanism requires the DR manager to assign a baseline to the participating consumer, where the baseline is an estimate of the counterfactual consumption of the consumer had it not been called to provide the DR service. A challenge in estimating baseline is the incentive the consumer has to inflate the baseline estimate. We consider the problem of learning online to estimate the baseline and to optimize the operating costs over a period of time under such incentives. We propose an online learning scheme that employs least-squares for estimation with a perturbation to the reward price (for the DR services or load curtailment) that is designed to balance the exploration and exploitation trade-off that arises with online learning. We show that, our proposed scheme is able to achieve a very low regret of $\mathcal{O}\left((\log{T})^2\right)$ with respect to the optimal operating cost over $T$ days of the DR program with full knowledge of the baseline, and is individually rational for the consumers to participate. Our scheme is significantly better than the averaging type approach, which only fetches $\mathcal{O}(T^{1/3})$ regret.

Ruijie Du, Deepan Muthirayan, Pramod P. Khargonekar et al.

Machine learning (ML) has demonstrated remarkable capabilities across many real-world systems, from predictive modeling to intelligent automation. However, the widespread integration of machine learning also makes it necessary to ensure machine learning-driven decision-making systems do not violate ethical principles and values of society in which they operate. As ML-driven decisions proliferate, particularly in cases involving sensitive attributes such as gender, race, and age, to name a few, the need for equity and impartiality has emerged as a fundamental concern. In situations demanding real-time decision-making, fairness objectives become more nuanced and complex: instantaneous fairness to ensure equity in every time slot, and long-term fairness to ensure fairness over a period of time. There is a growing awareness that real-world systems that operate over long periods and require fairness over different timelines. However, existing approaches mainly address dynamic costs with time-invariant fairness constraints, often disregarding the challenges posed by time-varying fairness constraints. To bridge this gap, this work introduces a framework for ensuring long-term fairness within dynamic decision-making systems characterized by time-varying fairness constraints. We formulate the decision problem with fairness constraints over a period as a constrained online optimization problem. A novel online algorithm, named LoTFair, is presented that solves the problem 'on the fly'. We prove that LoTFair can make overall fairness violations negligible while maintaining the performance over the long run.

Deepan Muthirayan, Jianjun Yuan, Dileep Kalathil et al.

We study the problem of online learning in predictive control of an unknown linear dynamical system with time varying cost functions which are unknown apriori. Specifically, we study the online learning problem where the control algorithm does not know the true system model and has only access to a fixed-length (that does not grow with the control horizon) preview of the future cost functions. The goal of the online algorithm is to minimize the dynamic regret, defined as the difference between the cumulative cost incurred by the algorithm and that of the best sequence of actions in hindsight. We propose two different online Model Predictive Control (MPC) algorithms to address this problem, namely Certainty Equivalence MPC (CE-MPC) algorithm and Optimistic MPC (O-MPC) algorithm. We show that under the standard stability assumption for the model estimate, the CE-MPC algorithm achieves $\mathcal{O}(T^{2/3})$ dynamic regret. We then extend this result to the setting where the stability assumption holds only for the true system model by proposing the O-MPC algorithm. We show that the O-MPC algorithm also achieves $\mathcal{O}(T^{2/3})$ dynamic regret, at the cost of some additional computation. We also present numerical studies to demonstrate the performance of our algorithm.

Arnav V. Malawade, Shih-Yuan Yu, Brandon Hsu et al.

In autonomous vehicles (AVs), early warning systems rely on collision prediction to ensure occupant safety. However, state-of-the-art methods using deep convolutional networks either fail at modeling collisions or are too expensive/slow, making them less suitable for deployment on AV edge hardware. To address these limitations, we propose sg2vec, a spatio-temporal scene-graph embedding methodology that uses Graph Neural Network (GNN) and Long Short-Term Memory (LSTM) layers to predict future collisions via visual scene perception. We demonstrate that sg2vec predicts collisions 8.11% more accurately and 39.07% earlier than the state-of-the-art method on synthesized datasets, and 29.47% more accurately on a challenging real-world collision dataset. We also show that sg2vec is better than the state-of-the-art at transferring knowledge from synthetic datasets to real-world driving datasets. Finally, we demonstrate that sg2vec performs inference 9.3x faster with an 88.0% smaller model, 32.4% less power, and 92.8% less energy than the state-of-the-art method on the industry-standard Nvidia DRIVE PX 2 platform, making it more suitable for implementation on the edge.

Trier Mortlock, Deepan Muthirayan, Shih-Yuan Yu et al.

Future manufacturing requires complex systems that connect simulation platforms and virtualization with physical data from industrial processes. Digital twins incorporate a physical twin, a digital twin, and the connection between the two. Benefits of using digital twins, especially in manufacturing, are abundant as they can increase efficiency across an entire manufacturing life-cycle. The digital twin concept has become increasingly sophisticated and capable over time, enabled by rises in many technologies. In this paper, we detail the cognitive digital twin as the next stage of advancement of a digital twin that will help realize the vision of Industry 4.0. Cognitive digital twins will allow enterprises to creatively, effectively, and efficiently exploit implicit knowledge drawn from the experience of existing manufacturing systems. They also enable more autonomous decisions and control, while improving the performance across the enterprise (at scale). This paper presents graph learning as one potential pathway towards enabling cognitive functionalities in manufacturing digital twins. A novel approach to realize cognitive digital twins in the product design stage of manufacturing that utilizes graph learning is presented.

Pratyush Muthukumar, Karishma Muthukumar, Deepan Muthirayan et al.

Generative adversarial imitation learning (GAIL) is a model-free algorithm that has been shown to provide strong results in imitating complex behaviors in high-dimensional environments. In this paper, we utilize the GAIL model for text generation to develop empathy-based context-aware conversational AI. Our model uses an expert trajectory of empathetic prompt-response dialogues which can accurately exhibit the correct empathetic emotion when generating a response. The Generator of the GAIL model uses the GPT-2 sequential pre-trained language model trained on 117 million parameters from 40 GB of internet data. We propose a novel application of an approach used in transfer learning to fine tune the GPT-2 model in order to generate concise, user-specific empathetic responses validated against the Discriminator. Our novel GAIL model utilizes a sentiment analysis history-based reinforcement learning approach to empathetically respond to human interactions in a personalized manner. We find that our model's response scores on various human-generated prompts collected from the Facebook Empathetic Dialogues dataset outperform baseline counterparts. Moreover, our model improves upon various history-based conversational AI models developed recently, as our model's performance over a sustained conversation of 3 or more interactions outperform similar conversational AI models.

Arnav V. Malawade, Nathan D. Costa, Deepan Muthirayan et al.

If machine failures can be detected preemptively, then maintenance and repairs can be performed more efficiently, reducing production costs. Many machine learning techniques for performing early failure detection using vibration data have been proposed; however, these methods are often power and data-hungry, susceptible to noise, and require large amounts of data preprocessing. Also, training is usually only performed once before inference, so they do not learn and adapt as the machine ages. Thus, we propose a method of performing online, real-time anomaly detection for predictive maintenance using Hierarchical Temporal Memory (HTM). Inspired by the human neocortex, HTMs learn and adapt continuously and are robust to noise. Using the Numenta Anomaly Benchmark, we empirically demonstrate that our approach outperforms state-of-the-art algorithms at preemptively detecting real-world cases of bearing failures and simulated 3D printer failures. Our approach achieves an average score of 64.71, surpassing state-of-the-art deep-learning (49.38) and statistical (61.06) methods.

Deepan Muthirayan, Pramod P. Khargonekar

In this paper we provide provable regret guarantees for an online meta-learning receding horizon control algorithm in an iterative control setting. We consider the setting where, in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and there are affine control input constraints. By analysing conditions under which sub-linear regret is achievable, we prove that the meta-learning online receding horizon controller achieves an average of the dynamic regret for the controller cost that is $\tilde{O}((1+1/\sqrt{N})T^{3/4})$ with the number of iterations $N$. Thus, we show that the worst regret for learning within an iteration improves with experience of more iterations, with guarantee on rate of improvement.

Shih-Yuan Yu, Arnav V. Malawade, Deepan Muthirayan et al.

Despite impressive advancements in Autonomous Driving Systems (ADS), navigation in complex road conditions remains a challenging problem. There is considerable evidence that evaluating the subjective risk level of various decisions can improve ADS' safety in both normal and complex driving scenarios. However, existing deep learning-based methods often fail to model the relationships between traffic participants and can suffer when faced with complex real-world scenarios. Besides, these methods lack transferability and explainability. To address these limitations, we propose a novel data-driven approach that uses scene-graphs as intermediate representations. Our approach includes a Multi-Relation Graph Convolution Network, a Long-Short Term Memory Network, and attention layers for modeling the subjective risk of driving maneuvers. To train our model, we formulate this task as a supervised scene classification problem. We consider a typical use case to demonstrate our model's capabilities: lane changes. We show that our approach achieves a higher classification accuracy than the state-of-the-art approach on both large (96.4% vs. 91.2%) and small (91.8% vs. 71.2%) synthesized datasets, also illustrating that our approach can learn effectively even from smaller datasets. We also show that our model trained on a synthesized dataset achieves an average accuracy of 87.8% when tested on a real-world dataset compared to the 70.3% accuracy achieved by the state-of-the-art model trained on the same synthesized dataset, showing that our approach can more effectively transfer knowledge. Finally, we demonstrate that the use of spatial and temporal attention layers improves our model's performance by 2.7% and 0.7% respectively, and increases its explainability.

Deepan Muthirayan, Pramod Khargonekar

In this work we provide provable regret guarantees for an online meta-learning control algorithm in an iterative control setting, where in each iteration the system to be controlled is a linear deterministic system that is different and unknown, the cost for the controller in an iteration is a general additive cost function and the control input is required to be constrained, which if violated incurs an additional cost. We prove (i) that the algorithm achieves a regret for the controller cost and constraint violation that are $O(T^{3/4})$ for an episode of duration $T$ with respect to the best policy that satisfies the control input control constraints and (ii) that the average of the regret for the controller cost and constraint violation with respect to the same policy vary as $O((1+\log(N)/N)T^{3/4})$ with the number of iterations $N$, showing that the worst regret for the learning within an iteration continuously improves with experience of more iterations.