Jeremy Carleton

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.

Jeremy Carleton, Debajoy Mukherjee, Srinivas Shakkottai et al.

Large Language Models (LLMs) are increasingly deployed across diverse applications that demand balancing multiple, often conflicting, objectives -- such as helpfulness, harmlessness, or humor. Aligning outputs to user-specific preferences in such multi-objective settings typically requires fine-tuning models for each objective or preference configuration, which is computationally expensive and inflexible. We introduce MAVIS -- Multi-Objective Alignment via Value-Guided Inference-Time Search -- a lightweight inference-time alignment framework that enables dynamic control over LLM behavior without modifying the base model's weights. MAVIS trains a set of small value models, each corresponding to a distinct objective. At inference time, these value models are combined using user-specified weights to produce a tilting function that adjusts the base model's output distribution toward desired trade-offs. The value models are trained using a simple iterative algorithm that ensures monotonic improvement of the KL-regularized policy. We show empirically that MAVIS outperforms baselines that fine-tune per-objective models and combine them post hoc, and even approaches the performance of the idealized setting where models are fine-tuned for a user's exact preferences.