Agent comparisons need matched resource rules and complete execution cohorts
Define multidimensional budgets, count failed-run costs, and compare success-cost tradeoffs without treating a normalized scalar as a substitute for matched experiments.
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The question for today
What you’ll understand
- Specify token, tool, time, and human-intervention resource boundaries.
- Calculate complete-cohort success and total cost per verified success.
- Explain why different budgets, censored attempts, and oracle selection can invalidate a claimed policy ranking.
An agent allowed many retries, parallel candidates, long tool execution, or extra human help solves a different resource-constrained problem from one given a single short attempt. Success rates should be tied to those conditions. A cost-normalized score can be useful, but it does not make unlike experiments equivalent or reveal every latency and reliability tradeoff. Keep the scheduled cohort complete and measure all consumed work, including failed attempts and selection, before claiming that one system is more efficient.
A resource budget is a contract, often with several dimensions
Record model input and output tokens, tool calls, tool compute, elapsed time, parallel workers, retrieval, verifier work, and human intervention where relevant. A wall-clock limit can reward parallelism that consumes much more total compute, while a token limit can hide expensive browser or code-execution actions. Define what happens at each limit and whether unfinished effects are reconciled before grading. Keep policy revision, hardware, service versions, and observation interface fixed or explicitly report differences. A benchmark name alone does not identify these resource conditions.
Do not infer a bounded-run outcome by deleting the expensive suffix of a completed trace unless that counterfactual is actually valid. A policy operating with a shorter budget may choose different actions, and a truncated task may leave asynchronous effects unfinished. Run the intended bounded policy and grade its state under the declared termination contract. If setup failures receive a separate category, predeclare that rule and report its count alongside scheduled and graded attempts. Excluding timeouts or invalid outputs after seeing them creates a success-only cohort rather than a fair comparison.
Count all costs and keep incompatible tradeoffs visible
Use an explicit cost model with its time and price version when converting resources into one scalar. Tokens, tool actions, and elapsed time are not naturally interchangeable units. Report the raw resource vector as well as any weighted cost so another reader can apply a different constraint. For repeated-candidate systems, include failed candidates and the mechanism used to select or verify the final one. A hidden evaluation oracle is not a free deployment component, and a system that cannot recognize its successful candidate may not achieve its reported one-of-k rate operationally.
Total cost per verified success divides all consumed cohort cost by verified successes, not merely the cost of successful runs. It is undefined when there are no successes. Even a properly computed ratio does not reveal tail latency, critical failures, or whether one system dominates another across every budget. Plot or tabulate success under several matched budgets where useful and identify tradeoffs rather than forcing a universal ranking. Selection of a preferred operating point should reflect the actual application objective and the limits of the measured task distribution.
Compare paired tasks and report the operating conditions
Use the same task versions and initial-state rules, with repeated seeds or conditions paired where that design is justified. Keep task families together in uncertainty analysis and disclose benchmark selection or tuning. A higher rate under twice the budget is evidence for that operating point, not necessarily a better policy at the smaller budget. Report interrupted and unfinished work, environment errors, and whether results come from one attempt or a multi-attempt strategy. AgentBench and SWE-bench provide task-driven evaluation settings, while the experiment's resource and cohort definitions still need explicit reporting.
The optimization lab illustrates comparison under an equal update count. Reset, explicitly set BOTH η=0.5 and x₀=2, predict x=0.125 after four updates, then Play or Step four times to t=2. Reset and re-set BOTH η=2.1 and x₀=2; predict x=2.9282. Edits retain t; n=min(1000000,floor(2 t)), and values beyond |x|=4 are explicitly out of range. This fixed quadratic descent has no agent tasks, token costs, verifiers, or deployment score. Equal modeled updates expose a parameter effect here without normalizing a real agent experiment.
Work it through
A higher success rate can require a different operating point
Two fictional systems each complete the same one-hundred-task scheduled cohort under their declared protocols. A has sixty verified successes and consumes ten thousand cost units across all runs. B has seventy successes and consumes twenty thousand units. No failure costs have been omitted.
A's success rate is 60/100=0.6 and B's is 70/100=0.7. B has ten percentage points more success at the stated, different resource conditions.
A costs 10000/60≈166.67 units per verified success; B costs 20000/70≈285.71. These ratios include failed runs and describe another tradeoff, not an automatic winner.
Neither point dominates on both success and total cost. To claim superiority under a fifteen-thousand-unit cohort budget, run the policies under a comparable enforced allocation rather than assume B's twenty-thousand-unit result transfers unchanged.
Complete cost accounting clarifies an operating-point tradeoff while matched experiments remain necessary for a fixed-budget capability claim.
The living notebook
Explore the model
Interactive lab · optimization
Equal update counts isolate one toy algorithmic choice
For EACH run Reset, set BOTH η and x₀, predict, then Play or Step four times to t=2/n=4. From x₀=2, η=0.5 gives x=0.125; η=2.1 gives 2.9282. Edits retain t; n is capped at 1000000 and |x|>4 is reported out of range. This quadratic solver has no agent, tool budget, evaluation cohort, or cost normalization.
- Position x0
- 2
- Objective x²/2
- 2
- Iteration behavior
- Stable step
Gradient descent on f(x) = x²/2: xₙ = (1 − η)ⁿx₀. Playback advances two discrete iterations per second. Values outside |x| ≤ 4 are explicitly reported. Parameter changes pause playback and recompute the model at the current elapsed time. Reset restores both parameters and returns time to zero. Playback starts paused. Adjust either parameter, then choose Play or Step.
Look forComparison requires explicit resource boundaries; a small analytic solver does not normalize an agent's complete execution cost.
Pause & reason
Check your understanding
Your turn
Try it yourself
A forty-trial fixed cohort has twenty verified successes and two thousand total cost units. Calculate success rate and cost per success. If successful trials averaged fifty units each, would reporting only that fifty-unit average account for the full strategy?
Take a moment to make a prediction or work it out on paper. Open a hint when you need one.
Give me a hint
The numerator for cohort cost includes all trials, not only those that passed.
Compare with the solution
Success rate is 20/40=0.5 and total cost per success is 2000/20=100 units. The fifty-unit successful-only average omits the cost of failures and therefore does not describe the resources spent to obtain the cohort's successes. Report both raw cost conditions and the complete-cohort ratio.
Keep the idea
Take it with you
- Budgets include tool, time, token, parallelism, and human-work boundaries.
- Complete-cohort costs include failures, retries, and selection.
- Normalized ratios clarify tradeoffs but do not replace matched-budget task experiments.
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