Ant Colony Optimization (ACO) is a meta-heuristic algorithm that has been successfully applied to various Combinatorial Optimization Problems (COPs).

There are two main challenges in solving AFT: 1) efficient feature transformation in a massive discrete search space; 2) robust feature transformation in an open learning environment.

We also provide theoretical guarantees in terms of convergence and generalization.

In Euclidean space, OCO boasts a robust theoretical foundation and numerous real-world applications, such as online load balancing (Molinaro, 2017), optimal control (Li et al., 2019), revenue maximization (Lin et al., 2019), and portfolio management (Jézéquel et al., 2022).

The continuous nature of belief states in POMDPs presents significant computational challenges in learning the optimal policy. In this paper, we consider an approach that solves a Partially Observable Reinforcement Learning (PORL) problem by approximating the corresponding POMDP model into a finite-state Markov Decision Process (MDP) (called Superstate MDP). We first derive theoretical guarantees that improve upon prior work that relate the optimal value function of the transformed Superstate MDP to the optimal value function of the original POMDP. Next, we propose a policy-based learning approach with linear function approximation to learn the optimal policy for the Superstate MDP. Consequently, our approach shows that a POMDP can be approximately solved using TD-learning followed by Policy Optimization by treating it as an MDP, where the MDP state corresponds to a finite history. We show that the approximation error decreases exponentially with the length of this history. To the best of our knowledge, our finite-time bounds are the first to explicitly quantify the error introduced when applying standard TD learning to a setting where the true dynamics are not Markovian.

Large language models (LLMs) still struggle across tasks outside of high-resource languages. In this work, we investigate cross-lingual transfer to lower-resource languages where task-specific post-training data is scarce. Building on prior work, we first validate that the subsets of model parameters that matter most for mathematical reasoning and multilingual capabilities are distinctly non-overlapping. To exploit this implicit separability between task and target language parameterization, we develop and analyze numerous modular frameworks to improve the composition of the two during fine-tuning. These methods generally employ freezing parameters or post hoc model merging to assign math and language improvement to different key parts of the LLM. In the absence of in-language math data, we demonstrate that the modular approaches successfully improve upon baselines across three languages, four models, and two fine-tuning paradigms (full and LoRA). Furthermore, we identify the most consistently successful modular method to be fine-tuning separate language and math experts and model merging via Layer-Swapping, somewhat surprisingly. We offer possible explanations for this result via recent works on the linearity of task vectors. We further explain this by empirically showing that reverting less useful fine-tuning updates after training often outperforms freezing them from the start.

Large Language Models (LLMs) are increasingly deployed in multi-turn conversational applications, where the management of the Key-Value (KV) Cache presents a significant bottleneck. The linear growth of the KV Cache with dialogue history imposes substantial computational costs, and existing eviction strategies often degrade performance by repeatedly compressing early conversational context, leading to information loss and context forgetting. This paper introduces FlowKV, a novel \textbf{multi-turn isolation mechanism} for KV Cache management, which can be applied to any KV Cache compression method without training. FlowKV's core innovation is a multi-turn isolation mechanism that preserves the accumulated compressed KV cache from past turns. Compression is then strategically applied only to the newly generated KV pairs of the latest completed turn, effectively preventing the re-compression of older context and thereby mitigating catastrophic forgetting. Our results demonstrate that FlowKV consistently and significantly outperforms baseline strategies in maintaining instruction-following accuracy and user preference retention from 10.90\% to 75.40\%, particularly in later conversational turns.