Dheeraj Narasimha

Jeremy Carleton, Prathik Vijaykumar, Divyanshu Saxena et al.

We address the challenge of zeroth-order online convex optimization where the objective function's gradient exhibits sparsity, indicating that only a small number of dimensions possess non-zero gradients. Our aim is to leverage this sparsity to obtain useful estimates of the objective function's gradient even when the only information available is a limited number of function samples. Our motivation stems from the optimization of large-scale queueing networks that process time-sensitive jobs. Here, a job must be processed by potentially many queues in sequence to produce an output, and the service time at any queue is a function of the resources allocated to that queue. Since resources are costly, the end-to-end latency for jobs must be balanced with the overall cost of the resources used. While the number of queues is substantial, the latency function primarily reacts to resource changes in only a few, rendering the gradient sparse. We tackle this problem by introducing the Compressive Online Gradient Optimization framework which allows compressive sensing methods previously applied to stochastic optimization to achieve regret bounds with an optimal dependence on the time horizon without the full problem dimension appearing in the bound. For specific algorithms, we reduce the samples required per gradient estimate to scale with the gradient's sparsity factor rather than its full dimensionality. Numerical simulations and real-world microservices benchmarks demonstrate CONGO's superiority over gradient descent approaches that do not account for sparsity.

Sarat Chandra Bobbili, Ujwal Dinesha, Dheeraj Narasimha et al.

Inference-time alignment enables large language models (LLMs) to generate outputs aligned with end-user preferences without further training. Recent post-training methods achieve this by using small guidance models to modify token generation during inference. These methods typically optimize a reward function KL-regularized by the original LLM taken as the reference policy. A critical limitation, however, is their dependence on a pre-trained reward model, which requires fitting to human preference feedback--a potentially unstable process. In contrast, we introduce PITA, a novel framework that integrates preference feedback directly into the LLM's token generation, eliminating the need for a reward model. PITA learns a small preference-based guidance policy to modify token probabilities at inference time without LLM fine-tuning, reducing computational cost and bypassing the pre-trained reward model dependency. The problem is framed as identifying an underlying preference distribution, solved through stochastic search and iterative refinement of the preference-based guidance model. We evaluate PITA across diverse tasks, including mathematical reasoning and sentiment classification, demonstrating its effectiveness in aligning LLM outputs with user preferences.