Arman C. Kizilkale

Arman C. Kizilkale, Rabih Salhab, Roland P. Malhame

Pressure on ancillary reserves, i.e.frequency preserving, in power systems has significantly mounted due to the recent generalized increase of the fraction of (highly fluctuating) wind and solar energy sources in grid generation mixes. The energy storage associated with millions of individual customer electric thermal (heating-cooling) loads is considered as a tool for smoothing power demand/generation imbalances. The piecewise constant level tracking problem of their collective energy content is formulated as a linear quadratic mean field game problem with integral control in the cost coefficients. The introduction of integral control brings with it a robustness potential to mismodeling, but also the potential of cost coefficient unboundedness. A suitable Banach space is introduced to establish the existence of Nash equilibria for the corresponding infinite population game, and algorithms are proposed for reliably computing a class of desirable near Nash equilibria. Numerical simulations illustrate the flexibility and robustness of the approach.

Arman C. Kizilkale, Shie Mannor

We analyze the efficiency of markets with friction, particularly power markets. We model the market as a dynamic system with $(d_t;\,t\geq 0)$ the demand process and $(s_t;\,t\geq 0)$ the supply process. Using stochastic differential equations to model the dynamics with friction, we investigate the efficiency of the market under an integrated expected undiscounted cost function solving the optimal control problem. Then, we extend the setup to a game theoretic model where multiple suppliers and consumers interact continuously by setting prices in a dynamic market with friction. We investigate the equilibrium, and analyze the efficiency of the market under an integrated expected social cost function. We provide an intriguing efficiency-volatility no-free-lunch trade-off theorem.

Isaac Chung, Phat Vo, Arman C. Kizilkale et al.

Retrieval Augmented Generation (RAG) is a common method for integrating external knowledge into pretrained Large Language Models (LLMs) to enhance accuracy and relevancy in question answering (QA) tasks. However, prompt engineering and resource efficiency remain significant bottlenecks in developing optimal and robust RAG solutions for real-world QA applications. Recent studies have shown success in using fine tuning to address these problems; in particular, Retrieval Augmented Fine Tuning (RAFT) applied to smaller 7B models has demonstrated superior performance compared to RAG setups with much larger models such as GPT-3.5. The combination of RAFT with parameter-efficient fine tuning (PEFT) techniques, such as Low-Rank Adaptation (LoRA), promises an even more efficient solution, yet remains an unexplored area. In this work, we combine RAFT with LoRA to reduce fine tuning and storage requirements and gain faster inference times while maintaining comparable RAG performance. This results in a more compute-efficient RAFT, or CRAFT, which is particularly useful for knowledge-intensive QA tasks in resource-constrained environments where internet access may be restricted and hardware resources limited.