Effective Reinforcement Learning for Reasoning in Language Models

Reinforcement learning (RL) has emerged as a promising strategy for improving the reasoning capabilities of language models (LMs) in domains such as mathematics and coding. However, most modern RL algorithms were designed to target robotics applications, which differ significantly from LM reasoning. We analyze RL algorithm design decisions for LM reasoning, for both accuracy and computational efficiency, focusing on relatively small models due to computational constraints. Our findings are: (i) on-policy RL significantly outperforms supervised fine-tuning (SFT), (ii) PPO-based off-policy updates increase accuracy instead of reduce variance, and (iii) removing KL divergence can lead to more concise generations and higher accuracy. Furthermore, we find that a key bottleneck to computational efficiency is that the optimal batch sizes for inference and backpropagation are different. We propose a novel algorithm, DASH, that performs preemptive sampling (i.e., sample a large batch and accumulate gradient updates in small increments), and gradient filtering (i.e., drop samples with small advantage estimates). We show that DASH reduces training time by 83% compared to a standard implementation of GRPO without sacrificing accuracy. Our findings provide valuable insights on designing effective RL algorithms for LM reasoning.

LLM Program Optimization via Retrieval Augmented Search

With the advent of large language models (LLMs), there has been a great deal of interest in applying them to solve difficult programming tasks. Recent work has demonstrated their potential at program optimization, a key challenge in programming languages research. We propose a blackbox adaptation method called Retrieval Augmented Search (RAS) that performs beam search over candidate optimizations; at each step, it retrieves in-context examples from a given training dataset of slow-fast program pairs to guide the LLM. Critically, we find that performing contextual retrieval based on an LLM-generated natural language description significantly outperforms retrieval based on the source code. In addition, we propose a method called AEGIS for improving interpretability by decomposing training examples into "atomic edits" that are significantly more incremental in nature. We show that RAS performs 1.8$\times$ better than prior state-of-the-art blackbox adaptation strategies, and that AEGIS performs 1.37$\times$ better while performing significantly smaller edits.

MathDSL: A Domain-Specific Language for Concise Mathematical Solutions Via Program Synthesis

We present MathDSL, a Domain-Specific Language (DSL) for mathematical equation solving, which, when deployed in program synthesis models, outperforms state-of-the-art reinforcement-learning-based methods. We also introduce a quantitative metric for measuring the conciseness of a mathematical solution and demonstrate the improvement in the quality of generated solutions compared to other methods. Our system demonstrates that a program synthesis system (DreamCoder) using MathDSL can generate programs that solve linear equations with greater accuracy and conciseness than using reinforcement learning systems. Additionally, we demonstrate that if we use the action spaces of previous reinforcement learning systems as DSLs, MathDSL outperforms the action-space-DSLs. We use DreamCoder to store equation-solving strategies as learned abstractions in its program library and demonstrate that by using MathDSL, these can be converted into human-interpretable solution strategies that could have applications in mathematical education.

CapText: Large Language Model-based Caption Generation From Image Context and Description

While deep-learning models have been shown to perform well on image-to-text datasets, it is difficult to use them in practice for captioning images. This is because captions traditionally tend to be context-dependent and offer complementary information about an image, while models tend to produce descriptions that describe the visual features of the image. Prior research in caption generation has explored the use of models that generate captions when provided with the images alongside their respective descriptions or contexts. We propose and evaluate a new approach, which leverages existing large language models to generate captions from textual descriptions and context alone, without ever processing the image directly. We demonstrate that after fine-tuning, our approach outperforms current state-of-the-art image-text alignment models like OSCAR-VinVL on this task on the CIDEr metric.