Apurv Shukla

Santosh Kumar Yadav, Apurv Shukla, Kamlesh Tiwari et al.

Pose recognition deals with designing algorithms to locate human body joints in a 2D/3D space and run inference on the estimated joint locations for predicting the poses. Yoga poses consist of some very complex postures. It imposes various challenges on the computer vision algorithms like occlusion, inter-class similarity, intra-class variability, viewpoint complexity, etc. This paper presents YPose, an efficient deep convolutional neural network (CNN) model to recognize yoga asanas from RGB images. The proposed model consists of four steps as follows: (a) first, the region of interest (ROI) is segmented using segmentation based approaches to extract the ROI from the original images; (b) second, these refined images are passed to a CNN architecture based on the backbone of EfficientNets for feature extraction; (c) third, dense refinement blocks, adapted from the architecture of densely connected networks are added to learn more diversified features; and (d) fourth, global average pooling and fully connected layers are applied for the classification of the multi-level hierarchy of the yoga poses. The proposed model has been tested on the Yoga-82 dataset. It is a publicly available benchmark dataset for yoga pose recognition. Experimental results show that the proposed model achieves the state-of-the-art on this dataset. The proposed model obtained an accuracy of 93.28%, which is an improvement over the earlier state-of-the-art (79.35%) with a margin of approximately 13.9%. The code will be made publicly available.

Apurv Shukla, Debabrota Basu

We study the preference-based pure exploration problem for bandits with vector-valued rewards. The rewards are ordered using a (given) preference cone $\mathcal{C}$ and our goal is to identify the set of Pareto optimal arms. First, to quantify the impact of preferences, we derive a novel lower bound on sample complexity for identifying the most preferred policy with a confidence level $1-δ$. Our lower bound elicits the role played by the geometry of the preference cone and punctuates the difference in hardness compared to existing best-arm identification variants of the problem. We further explicate this geometry when the rewards follow Gaussian distributions. We then provide a convex relaxation of the lower bound and leverage it to design the Preference-based Track and Stop (PreTS) algorithm that identifies the most preferred policy. Finally, we show that the sample complexity of PreTS is asymptotically tight by deriving a new concentration inequality for vector-valued rewards.

Udvas Das, Apurv Shukla, Debabrota Basu

Preference-based Pure Exploration (PrePEx) aims to identify with a given confidence level the set of Pareto optimal arms in a vector-valued (aka multi-objective) bandit, where the reward vectors are ordered via a (given) preference cone $\mathcal{C}$. Though PrePEx and its variants are well-studied, there does not exist a computationally efficient algorithm that can optimally track the existing lower bound for arbitrary preference cones. We successfully fill this gap by efficiently solving the minimisation and maximisation problems in the lower bound. First, we derive three structural properties of the lower bound that yield a computationally tractable reduction of the minimisation problem. Then, we deploy a Frank-Wolfe optimiser to accelerate the maximisation problem in the lower bound. Together, these techniques solve the maxmin optimisation problem in $\mathcal{O}(KL^{2})$ time for a bandit instance with $K$ arms and $L$ dimensional reward, which is a significant acceleration over the literature. We further prove that our proposed PrePEx algorithm, FraPPE, asymptotically achieves the optimal sample complexity. Finally, we perform numerical experiments across synthetic and real datasets demonstrating that FraPPE achieves the lowest sample complexities to identify the exact Pareto set among the existing algorithms.

Apurv Shukla, P. R. Kumar

We consider contextual bandit learning under distribution shift when reward vectors are ordered according to a given preference cone. We propose an adaptive-discretization and optimistic elimination based policy that self-tunes to the underlying distribution shift. To measure the performance of this policy, we introduce the notion of preference-based regret which measures the performance of a policy in terms of distance between Pareto fronts. We study the performance of this policy by establishing upper bounds on its regret under various assumptions on the nature of distribution shift. Our regret bounds generalize known results for the existing case of no distribution shift and vectorial reward settings, and scale gracefully with problem parameters in presence of distribution shifts.

Apurv Shukla

We consider a high-dimensional stochastic contextual linear bandit problem when the parameter vector is $s_{0}$-sparse and the decision maker is subject to privacy constraints under both central and local models of differential privacy. We present PrivateLASSO, a differentially private LASSO bandit algorithm. PrivateLASSO is based on two sub-routines: (i) a sparse hard-thresholding-based privacy mechanism and (ii) an episodic thresholding rule for identifying the support of the parameter $θ$. We prove minimax private lower bounds and establish privacy and utility guarantees for PrivateLASSO for the central model under standard assumptions.

Daniel Bienstock, Minchan Jeong, Apurv Shukla et al.

We consider streaming principal component analysis when the stochastic data-generating model is subject to perturbations. While existing models assume a fixed covariance, we adopt a robust perspective where the covariance matrix belongs to a temporal uncertainty set. Under this setting, we provide fundamental limits on convergence of any algorithm recovering principal components. We analyze the convergence of the noisy power method and Oja's algorithm, both studied for the stationary data generating model, and argue that the noisy power method is rate-optimal in our setting. Finally, we demonstrate the validity of our analysis through numerical experiments on synthetic and real-world dataset.