REAL Loss: Optimizing Real Expected Acceptance Length for Speculative Decoding

Speculative decoding accelerates LLM inference by having a draft model propose multiple tokens for the target model to verify in one pass. The speedup is governed by the expected acceptance length (EAL), yet standard training objectives such as cross-entropy, KL divergence, and total variation focus only on distribution matching or single-step overlap. Recent studies instead propose block-level training objectives, aiming to optimize EAL directly. However, these objectives remain surrogates rather than exact formulations of EAL. For example, some average later acceptance over target-distributed continuations rather than the verification branches selected by accepted tokens, introducing a covariance gap that can reverse the gradient direction. We analyze this gap and derive REAL, a real EAL training loss that uses path weights for unbiased estimation and Rao-Blackwellization for variance…