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Nov 4

Oracle-Efficient and Parameter-Free Agnostic Smoothed Online Learning

Online learning is an attractive framework in many domains because it permits well-defined learning even when data are dependent or chosen adversarially. This generality, however, comes at a steep price, introducing significant statistical and computational barriers. Recently, smoothed online learning has emerged as a promising framework that interpolates between the fully adversarial and fully stochastic settings by assuming that the conditional law of each covariate has density at most 1/σ with respect to some fixed base measure μ, and it is known to match the statistical and computational guarantees of classical learning while still allowing for much of the flexibility of online learning. However, existing oracle-efficient algorithms require either (i) sampling access to the base measure μ or (ii) labels that are perfectly predicted by a fixed hypothesis. Both assumptions limit the applicability of these algorithms, in contrast to statistical learning, where empirical risk minimization (ERM) learns efficiently in the agnostic setting without any knowledge of the data distribution. We show that neither assumption is necessary, giving the first oracle-efficient algorithm that achieves sublinear regret in the agnostic setting without knowledge of μ. Our algorithm, based on Gaussian Follow-The-Perturbed-Leader, is parameter-free: it requires no knowledge of μ, the smoothing parameter σ, or the horizon T, and it achieves regret widetilde O(dT/σ) for binary classes of VC dimension d with a single call to an ERM oracle per round, which is optimal up to a d factor. En route to establishing the regret bound, we introduce several new techniques that may be of independent interest.

  • 4 authors
·
Oct 6

Think First, Diffuse Fast: Improving Diffusion Language Model Reasoning via Autoregressive Plan Conditioning

Diffusion large language models (dLLMs) generate text via iterative denoising but consistently underperform on multi-step reasoning. We hypothesize this gap stems from a coordination problem: AR models build coherence token-by-token, while diffusion models must coordinate all positions simultaneously. We propose plan conditioning, a training-free method that prepends a short (~100-token) natural-language plan from an AR model to the diffusion model's prompt. The plan serves as a frozen scaffold -- globally visible context that every token position can attend to from the first denoising step. On GSM8K, plan conditioning improves LLaDA-8B-Instruct from 75.6% to 87.2% (+11.6 percentage points), matching a same-size AR model (LLaMA 3.1 8B, 87.7%) despite a 6.4pp weaker baseline. On HumanEval, the gain is +12.8pp (37.2% to 50.0%), showing plans generalize to code. The same plans improve LLaMA by only +5.7pp on GSM8K and +1.3pp on HumanEval -- diffusion models benefit 2-10x more, supporting the coordination-problem hypothesis. Across 5 random seeds, plan-conditioned GSM8K accuracy has zero standard deviation, making diffusion inference highly stable. Ablations reveal the model follows plan strategy (wrong-strategy plans cause -16.3pp) but is robust to plan values (perturbed numbers: -1.1pp), and that planner quality has a sharp threshold: smaller Llama-class plans hurt (-1.6 to -6.8pp) while frontier plans provide the full lift. Attention analysis confirms the mechanism: plan tokens receive 1.8x excess attention during early denoising, declining to uniform as completion tokens solidify. Plan conditioning costs ~$0.002 per problem and adds ~2s of latency.

  • 1 authors
·
Feb 19