Srujan Teja Thomdapu

Zeeshan Akhtar, Amrit Singh Bedi, Srujan Teja Thomdapu et al.

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where the objective function depends on the solution of another stochastic optimization problem. The proposed $\textbf{S}$tochastic $\textbf{Bi}$-level $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SBFW}$) algorithm can be applied to streaming settings and does not make use of large batches or checkpoints. The sample complexity of SBFW is shown to be $\mathcal{O}(ε^{-3})$ for convex objectives and $\mathcal{O}(ε^{-4})$ for non-convex objectives. Improved rates are derived for the stochastic compositional problem, which is a special case of the bi-level problem, and entails minimizing the composition of two expected-value functions. The proposed $\textbf{S}$tochastic $\textbf{C}$ompositional $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SCFW}$) is shown to achieve a sample complexity of $\mathcal{O}(ε^{-2})$ for convex objectives and $\mathcal{O}(ε^{-3})$ for non-convex objectives, at par with the state-of-the-art sample complexities for projection-free algorithms solving single-level problems. We demonstrate the advantage of the proposed methods by solving the problem of matrix completion with denoising and the problem of policy value evaluation in reinforcement learning.

Srujan Teja Thomdapu, Harshvardhan, Ketan Rajawat

This work studies constrained stochastic optimization problems where the objective and constraint functions are convex and expressed as compositions of stochastic functions. The problem arises in the context of fair classification, fair regression, and the design of queuing systems. Of particular interest is the large-scale setting where an oracle provides the stochastic gradients of the constituent functions, and the goal is to solve the problem with a minimal number of calls to the oracle. Owing to the compositional form, the stochastic gradients provided by the oracle do not yield unbiased estimates of the objective or constraint gradients. Instead, we construct approximate gradients by tracking the inner function evaluations, resulting in a quasi-gradient saddle point algorithm. We prove that the proposed algorithm is guaranteed to find the optimal and feasible solution almost surely. We further establish that the proposed algorithm requires $\mathcal{O}(1/ε^4)$ data samples in order to obtain an $ε$-approximate optimal point while also ensuring zero constraint violation. The result matches the sample complexity of the stochastic compositional gradient descent method for unconstrained problems and improves upon the best-known sample complexity results for the constrained settings. The efficacy of the proposed algorithm is tested on both fair classification and fair regression problems. The numerical results show that the proposed algorithm outperforms the state-of-the-art algorithms in terms of the convergence rate.

Srujan Teja Thomdapu, Palash Katiyar, Ketan Rajawat

The importance of content delivery networks (CDN) continues to rise with the exponential increase in the generation and consumption of electronic media. In order to ensure a high quality of experience, CDNs often deploy cache servers that are capable of storing some of the popular files close to the user. Such edge caching solutions not only increase the content availability, but also result in higher download rates and lower latency at the user. We consider the problem of content placement from an optimization perspective. Different from the classical eviction-based algorithms, the present work formulates the content placement problem from an optimization perspective and puts forth an online algorithm for the same. In contrast to the existing optimization-based solutions, the proposed algorithm is incremental and incurs very low computation cost, while yielding storage allocations that are provably near-optimal. The proposed algorithm can handle time varying content popularity, thereby obviating the need for periodically estimating demand distribution. Using synthetic and real IPTV data, we show that the proposed policies outperform all the state of art caching techniques in terms of various metrics.