Instructional Material
On the optimization dynamics of RLVR: Gradient gap and step size thresholds
Reinforcement Learning with Verifiable Rewards (RLVR), which uses simple binary feedback to post-train large language models, has shown significant empirical success. However, a principled understanding of why it works has been lacking. This paper builds a theoretical foundation for RLVR by analyzing its training process at both the full-response (trajectory) and token levels. Central to our analysis is a quantity called the Gradient Gap, which formalizes the direction of improvement from low-reward to high-reward regions of the response space. We prove that convergence critically depends on aligning the update direction with this Gradient Gap. Moreover, we derive a sharp step-size threshold based on the magnitude of the Gradient Gap: below it, learning converges, whereas above it, performance collapses. Our theory further predicts how the critical step size must scale with response length and the success rate, thereby explaining why practical heuristics such as length normalization improve stability and showing that, with a fixed learning rate, the success rate can stagnate strictly below $100\%$. We validate these predictions through controlled bandit simulations and LLM experiments, including training Qwen2.5-7B with GRPO.
From Handwriting to Feedback: Evaluating VLMs and LLMs for AI-Powered Assessment in Indonesian Classrooms
Aisyah, Nurul, Kautsar, Muhammad Dehan Al, Hidayat, Arif, Chowdhury, Raqib, Koto, Fajri
Despite rapid progress in vision-language and large language models (VLMs and LLMs), their effectiveness for AI-driven educational assessment in real-world, underrepresented classrooms remains largely unexplored. We evaluate state-of-the-art VLMs and LLMs on over 14K handwritten answers from grade-4 classrooms in Indonesia, covering Mathematics and English aligned with the local national curriculum. Unlike prior work on clean digital text, our dataset features naturally curly, diverse handwriting from real classrooms, posing realistic visual and linguistic challenges. Assessment tasks include grading and generating personalized Indonesian feedback guided by rubric-based evaluation. Results show that the VLM struggles with handwriting recognition, causing error propagation in LLM grading, yet LLM feedback remains pedagogically useful despite imperfect visual inputs, revealing limits in personalization and contextual relevance.
Bayesian Decision Making around Experts
Ornia, Daniel Jarne, Dyer, Joel, Bishop, Nicholas, Calinescu, Anisoara, Wooldridge, Michael
Complex learning agents are increasingly deployed alongside existing experts, such as human operators or previously trained agents. However, it remains unclear how should learners optimally incorporate certain forms of expert data, which may differ in structure from the learner's own action-outcome experiences. We study this problem in the context of Bayesian multi-armed bandits, considering: (i) offline settings, where the learner receives a dataset of outcomes from the expert's optimal policy before interaction, and (ii) simultaneous settings, where the learner must choose at each step whether to update its beliefs based on its own experience, or based on the outcome simultaneously achieved by an expert. We formalize how expert data influences the learner's posterior, and prove that pretraining on expert outcomes tightens information-theoretic regret bounds by the mutual information between the expert data and the optimal action. For the simultaneous setting, we propose an information-directed rule where the learner processes the data source that maximizes their one-step information gain about the optimal action. Finally, we propose strategies for how the learner can infer when to trust the expert and when not to, safeguarding the learner for the cases where the expert is ineffective or compromised. By quantifying the value of expert data, our framework provides practical, information-theoretic algorithms for agents to intelligently decide when to learn from others.