Dual-Budget Control for Search Agents¶

Dual-budget control lets a search agent under tool-call and token caps score each action by Value-of-Information per unit budget, spending next on the highest-ranking one.

The Two-Budget Problem¶

Search agents operate under two hard limits at inference time: a cap on tool calls and a cap on generated tokens. Both bind. Better answers do not come from a stronger model alone — they come from explicit control over which action receives the next budget unit and when accumulated evidence is sufficient to commit (Fang et al., 2026).

Three action classes compete for the same budget:

Retrieval — call a tool, spend a tool-call unit and the tokens for the result.
Decomposition — break the question into sub-queries, spend tokens but no tool call.
Commit — emit the final answer and stop.

A naive policy fires retrievals greedily until the tool-call cap or the token cap hits zero, the opposite of heuristic-based effort scaling. A dual-budget controller picks differently: it ranks actions by expected marginal task value per unit budget consumed, then spends greedily on the highest-ranking option.

Value-of-Information Scoring¶

Each candidate action gets a Value-of-Information (VOI) score: an operational estimate of marginal task value per unit budget under the current search state and remaining dual budget (Fang et al., 2026). The action with the highest VOI/cost ratio fires next.

graph TD
    A[Search State<br/>+ Remaining Budget] --> B[Score Each Action<br/>VOI per unit cost]
    B --> C{Highest VOI?}
    C -->|Retrieval| D[Tool Call]
    C -->|Decomposition| E[Generate Sub-Query]
    C -->|Commit| F[Final Answer]
    D --> A
    E --> A
    F --> G[Selective Finalizer]

The score depends on remaining budget, not just current state. A retrieval that looks valuable with 10 tool calls left may score below a commit when only 1 remains — because the marginal value of one more retrieval is bounded above by the probability it changes the answer, while the cost of running out of budget mid-trajectory is the whole task.

Snell et al. (2024) report the same causal structure for test-time compute scaling more broadly: a compute-optimal allocation that adapts per prompt improves test-time-compute efficiency by more than 4x over a best-of-N baseline. The pattern in both cases is difficulty-conditioned allocation beats uniform when budgets bind.

Selective Evidence-Grounded Finalizer¶

After the search trajectory ends, a finalizer compares the trajectory answer with a refined candidate. It rewrites only when the residual error appears to be a low-risk answer-form error — formatting, unit conversion, name disambiguation — not when retrieval was incomplete (Fang et al., 2026).

This guard matters because post-hoc rewriting can degrade near-ceiling outputs. The self-critique paradox shows critics drop accuracy from ~98% to ~57% on tasks where the base agent is already correct — see the inference-time tool-call reviewer for the same constraint applied to pre-dispatch review. The finalizer's "rewrite only on answer-form errors" rule is exactly the mitigation needed to keep the rewriter from overwriting correct retrievals with hallucinated revisions.

Ablations attribute the bulk of measured gains to the search-time controller (especially the budget-dependent penalty); the finalizer mainly helps when the retrieval path is already adequate (Fang et al., 2026).

What Belongs Where¶

Pattern	Allocates	Unit
Reasoning budget allocation	Reasoning compute by phase	Per workflow phase (plan / execute / verify)
Context budget allocation	Tokens within the window	Per loaded artifact
Dual-budget control (this page)	Remaining tool calls + tokens	Per candidate action
Inference-time tool-call reviewer	Approve/reject decisions	Per provisional tool call

These patterns are composable, not substitutes. A harness can run reasoning-budget allocation across phases, dual-budget control within the search phase, and a tool-call reviewer on each provisional dispatch — they operate at different slots in the loop.

When This Pattern Backfires¶

The pattern is valuable specifically when budgets bind. Skip it when:

Slack budgets. Agents that routinely complete tasks below the cap don't benefit — without binding constraints, VOI scoring is overhead. The optimisation surface only exists under tight budgets.
Single-hop or single-tool tasks. With one action class available, allocation collapses to early-stopping. Simpler heuristics already cover that.
Strong base models on light search. Answer-time control mainly helps when the retrieval path is already adequate (Fang et al., 2026) — when the base model rarely makes answer-form errors, the finalizer adds latency without revenue.
Hidden cost variance. VOI/cost ratios assume cost is observable. Retrieval calls with stochastic tail latency (rate limits, cold caches) make the score noisy and can mis-rank actions.
Harnesses without budget accounting. The controller needs (remaining_tool_calls, remaining_tokens) exposed every step. Harnesses that hide this state need instrumentation work before the pattern is implementable.

Example¶

A research agent answers multi-hop questions over a corpus with max_tool_calls=8 and max_tokens=4000. Three feasible actions at step 4 with (remaining_tool_calls=4, remaining_tokens=2200):

Action            Est. value gain   Est. cost      VOI / cost
retrieval(q3)     0.35              1 call + 400t  0.35 / (1/4 + 400/2200) = 0.81
decompose(q3)     0.20              0 calls + 200t 0.20 / (200/2200) = 2.20
commit(answer)    0.10              0 calls + 80t  0.10 / (80/2200) = 2.75

The controller fires commit because its VOI/cost ratio is highest given how little budget remains. With remaining_tool_calls=8 at step 0, the same retrieval would score above commit — the budget conditioning is what changes the ordering. A fixed greedy policy ignoring remaining budget would fire retrieval(q3) and risk hitting the cap before reaching a confident answer.

Key Takeaways¶

Search agents under hard caps on both tool calls and tokens face a per-action allocation problem, not a single-budget problem.
Score each candidate action by VOI per unit budget under current state and remaining budget; greedy selection on this score is the controller.
A selective finalizer should rewrite only on answer-form errors, never to overwrite a complete retrieval — otherwise it degrades correct outputs, the same hazard the inference-time tool-call reviewer guards against.
The pattern pays back where budgets bind. Slack budgets, single-hop tasks, and harnesses without budget accounting do not benefit.