AWhat changed
Could one search strategy be best for every optimization problem? Wolpert and Macready show why the answer changes when problems are averaged in a particular way. On finite search spaces, averaging uniformly over all objective functions removes the advantage of any strategy when performance depends on the values found after distinct queries. Practical success therefore depends on the structure of the problems encountered. This does not say that a useful optimizer, or a well-chosen benchmark, is impossible.
Scientific scope
Could one search strategy be best for every optimization problem? Wolpert and Macready show why the answer changes when problems are averaged in a particular way. On finite search spaces, averaging uniformly over all objective functions removes the advantage of any strategy when performance depends on the values found after distinct queries. Practical success therefore depends on the structure of the problems encountered. This does not say that a useful optimizer, or a well-chosen benchmark, is impossible. Finite search and cost-value sets, uniform all-function averaging and distinct oracle evaluations. Wall-clock runtime and arbitrary structured problem distributions are outside this equality. The time-dependent result has additional bijectivity restrictions. The 1997 optimization theorem is not a blanket statement that all learning algorithms perform equally in the real world.
Evidence
The linked original works support the scoped statement and contribution attribution. WRS has not independently replayed experiments or reconstructed a full mathematical proof. Finite search and cost-value sets, uniform all-function averaging and distinct oracle evaluations. Wall-clock runtime and arbitrary structured problem distributions are outside this equality. The time-dependent result has additional bijectivity restrictions. The 1997 optimization theorem is not a blanket statement that all learning algorithms perform equally in the real world.
Contributors
- The named authors in the research record · SCIENCE: Source-listed authors for the exact contribution; experimental subjects are not autonomous scientific authors. Source support and predecessor work retain separate roles. Individual effort shares and unresolved identities are not inferred.
Provisional WRS assessment, edition 2026-10-23.3. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.
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