Tengyang Xie
Publications
Breaking the Capability Ceiling of LLM Post-Training by Reintroducing Markov States
Reinforcement learning (RL) has become a standard paradigm for post-training and aligning Large Language Models (LLMs), yet recent evidence suggests it faces a persistent "capability ceiling": unlike classical RL systems that discover novel strategies, RL for LLMs often acts as a mere refiner of patterns already latent in pre-trained weights. In this work, we identify a fundamental structural bottleneck: while classical RL relies on compact, informative Markov states, current LLM post-training formulations are tethered to an ever-expanding history of actions. We revisit a classical principle long central to RL yet absent from LLM post-training: explicit Markov states. Theoretically, we provide rigorous guarantees demonstrating that leveraging estimated Markov states can significantly reduce sample complexity. Empirically, we show that introducing Markov states consistently breaks the performance boundaries of standard RL post-training across a suite of complex logic puzzles. Our findings suggest that moving beyond "history-as-state" modeling in favor of structured Markovian representations is essential for unlocking open-ended discovery and genuinely new reasoning capabilities in Generative AI.
POLCA: Stochastic Generative Optimization with LLM
Optimizing complex systems, ranging from LLM prompts to multi-turn agents, traditionally requires labor-intensive manual iteration. We formalize this challenge as a stochastic generative optimization problem where a generative language model acts as the optimizer, guided by numerical rewards and text feedback to discover the best system. We introduce Prioritized Optimization with Local Contextual Aggregation (POLCA), a scalable framework designed to handle stochasticity in optimization -- such as noisy feedback, sampling minibatches, and stochastic system behaviors -- while effectively managing the unconstrained expansion of solution space. POLCA maintains a priority queue to manage the exploration-exploitation tradeoff, systematically tracking candidate solutions and their evaluation histories. To enhance efficiency, we integrate an $\varepsilon$-Net mechanism to maintain parameter diversity and an LLM Summarizer to perform meta-learning across historical trials. We theoretically prove that POLCA converges to near-optimal candidate solutions under stochasticity. We evaluate our framework on diverse benchmarks, including $τ$-bench, HotpotQA (agent optimization), VeriBench (code translation) and KernelBench (CUDA kernel generation). Experimental results demonstrate that POLCA achieves robust, sample and time-efficient performance, consistently outperforming state-of-the-art algorithms in both deterministic and stochastic problems. The codebase for this work is publicly available at https://github.com/rlx-lab/POLCA.