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Plan and Budget: Effective and Efficient Test-Time Scaling on Reasoning Large Language Models

ICLR 2026 · Large language models › Reasoning and chain of thought · approach: Efficient and adaptive thinking · 0 citations (OpenAlex)

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Proposes Plan-and-Budget, a training-free test-time framework that decomposes queries into sub-questions and allocates token budgets via decay-based schedules, guided by a theoretical Budget Allocation Model, improving the efficiency score E^3 across MATH-500, NaturalInstructions, and TravelPlanner.

Problem

LLM reasoning is miscalibrated: overthinking wastes tokens on simple queries while fixed global token budgets cause underthinking on hard ones; existing efficiency metrics ignore accuracy.

Approach

Decompose a query into sub-questions with a lightweight planner, estimate per-sub-question complexity weights, and allocate the total token budget across sub-questions using decay-based schedules (polynomial, cosine, etc.), motivated by a power-law Budget Allocation Model; also introduces the E^3 = A^2/T metric.

Key results

• On TravelPlanner, DS-Qwen-32B's E^3 rises from 0.16 to 0.47 (+193.8%) with Plan-and-Budget, approaching DS-LLaMA-70B without planning (0.50).
• On MATH-500, Plan-and-Budget improves E^3 for DS-LLaMA-70B from 4.55 to 5.89 (+29.4%) and for o4-mini from 13.25 to 15.95 (+20.3%) while keeping accuracy comparable.
• On NaturalInstructions, E^3 improves by 19.3–36.0% over baselines, e.g., QwQ-32B from 1.47 to 2.00.

Surprising findings

• Global token budgets reduce tokens but also degrade pass rates on TravelPlanner across all difficulty levels, indicating underthinking.
• Longer generation can degrade quality; the authors argue excessive decoding can wander within the solution space.

Limitations

• Requires an additional LLM call to generate the decomposition plan.
• Budget allocation uses heuristic decay schedules rather than the estimated optimal BAM parameters, which are not directly observable.
• The theoretical derivation relies on approximations (e.g., greedy path as uncertainty proxy).

Experimental setup

Datasets: MATH-500 NaturalInstructions TravelPlanner

Benchmarks: MATH-500 NaturalInstructions TravelPlanner

Metrics: accuracy ROUGE hard constraint pass rate average tokens E^3 A/T

Baselines: Vanilla Global Budget Certaindex Planned Global Budget

Builds on: chain-of-thought self-consistency Certaindex

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