Read epsilon-constraint duals as frontier slope / exchange rate in multi-objective skill#1406
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Read epsilon-constraint duals as frontier slope / exchange rate in multi-objective skill#1406cafzal wants to merge 9 commits into
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…lti-objective skill Extends the dual/sensitivity work from NVIDIA#1393 into the multi-objective layer: the dual on a swept epsilon-constraint is the local slope of the Pareto frontier (the exchange rate between the two objectives), available off each LP/QP solve at no extra cost. - Step 3: note that the swept constraint's dual is the frontier's local tangent; defers "what duals are / which problem types expose them" to the formulation skill (no API symbols inlined). - Step 4: a practical-notes bullet to refine the sweep where the slope changes, spending fewer solves than a uniform grid (LP/QP; MILP falls back to gaps between primal objective values). - Step 5: the exchange rate is read from the dual on LP/QP (differencing on MILP), and the epsilon-constraint duals are the implicit weights per point. - evals: add a QP risk-return frontier task exercising dual-as-exchange-rate; clarify the MILP supplier eval to estimate the rate by differencing. Concepts/workflow skill: LP/QP-only scoping preserved, no maturity labels. BENCHMARK.md, the skill card, and the signature are regenerated by NVSkills CI. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
Addresses duality-review feedback (a PDLP co-author's lens). cuOpt's default LP method is Concurrent — it races PDLP (first-order), dual simplex, and barrier — so a returned dual is exact-basic only when dual simplex solved it and accurate only to the optimality tolerance otherwise. Three concepts-level, stale-robust edits (no method names in the skill text): - Step 5: drop "exact and local"; the exchange rate is the dual "accurate to the solve's optimality tolerance (tighten it before relying on a dual)." - Step 4: treat a slope change as a knee only when it exceeds the solve tolerance — smaller differences are solver noise, not curvature. - Step 5: at a knee the slope is two-sided; quote the exchange rate as a range. Consistent with the "PDLP-tolerance caveat" already noted in NVIDIA#1355. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
Verified against the cuOpt repo + docs. Two corrections: - cuOpt returns no dual variables for problems with quadratic constraints (docs/cuopt/source/cuopt-c/convex/convex-examples.rst). The skill offers a quadratic ε-constraint (xᵀQx ≤ ε) option, which would have no dual to read. Step 3 now says: read the dual off a *linear* ε-constraint — keep a quadratic objective as f1 and ε-constrain the linear objectives. - Switch the new eval from a QP risk-return frontier to an LP cost-vs-quality blend. LP duals are the tested, documented path (lp_duals asset); QP-dual reading is untested and the api-* skills scope duals to "LP only", so the eval should exercise the verified path. Skill prose stays "LP/QP" per the formulation skill. Separate (not in this PR): the formulation skill's "no quadratic constraints" is stale (cuOpt supports convex quadratic constraints via barrier/SOC), and the api-python/api-c "dual values (LP only)" likely needs "LP/QP, linear constraints" — flagged for follow-up. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
Reverts the over-conservative QP->LP eval switch. Git history confirms QP duals are real and recent: barrier extended for SOCP (NVIDIA#1290, 2026-05-30) and general convex quadratic constraints (NVIDIA#1361, 2026-06-02); the barrier solver is primal-dual and pdlp/solve.cu returns dual_solution + reduced_cost for the Barrier method. The api-python/api-c "dual values (LP only)" wording predates this (NVIDIA#1183, 2026-05-07) and is the stale part, not the formulation skill's "LP/QP" (NVIDIA#1393). The QP risk-return eval sweeps a *linear* return floor, whose dual is returned (cuOpt returns no dual for a quadratic constraint, so the quadratic stays the objective). Skill prose unchanged (already "LP/QP" + linear-constraint caveat). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
A zero shadow price means the constraint is slack (not binding), so during a sweep a zero dual on an ε-bound signals the objectives aren't trading off there — the sweep has run past the frontier's edge. Small precision/diagnostic addition; consistent with the dual-as-slope content already in Step 3. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
…vior cpp/src/pdlp/solve.cu (has_quadratic_constraints -> thrust::fill the entire dual_solution + reduced_cost with quiet_NaN) shows a single quadratic constraint suppresses duals for the *whole* solve, not just that constraint's row. Reword "no dual for a quadratic constraint" -> "any quadratic constraint makes cuOpt return no duals for the whole solve" in Step 3 and the QP eval, for consistency with PRs NVIDIA#1407 (formulation) and NVIDIA#1408 (api skills, "NaN-filled"). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
This was referenced Jun 8, 2026
Condense the dual-as-slope note to four non-overlapping points — what it is (slope/exchange rate/tangent, read off the solve free), the zero-dual=slack diagnostic, scope+fallback (LP/QP, linear ε-constraint only; MILP and quadratic constraints have none, so difference instead), and the formulation cross-ref. Same facts, ~20% shorter; drops "exact" (kept in Step 5 as "to solve tolerance"). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
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📝 WalkthroughWalkthroughThis pull request updates the multi-objective exploration skill documentation and evaluation cases to clarify when dual values from epsilon-constraint methods can interpret Pareto frontier exchange rates (LP/QP only) versus when differencing is required (MILP). It revises frontier refinement allocation to focus solves near dual-change knees for LP/QP and to use primal gaps for MILP, and strengthens reporting guidance with optimality caveats. ChangesMulti-objective frontier dual interpretation and evaluation alignment
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…barrier solver" - Step 5 cross-ref: "defines shadow price ..." -> "covers what duals mean and which problem types expose them". - Step 3 quadratic-constraint note: drop "the barrier solver" (the solve method isn't part of the dual contract); keep the second-order-cone constraint form. Consistent with the trim applied to the api-* skills in NVIDIA#1408. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
…ights wording - Step 3: drop "(Q positive semidefinite, inequality only)" — the sentence already says convex, shows the <= form, and the next sentence covers the non-convex/equality exclusion. Same over-specification flagged on the companion formulation PR. - Step 4: a dual jump between two solved points locates a bend between them, not necessarily the knee (Step 5 defines the knee as the sharpest bend). - Step 5: weighted-sum with the epsilon-duals as weights reproduces that tradeoff, not necessarily the identical point (flat segments tie). Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com> Signed-off-by: cafzal <cameron.afzal@gmail.com>
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Description
Adds dual-value guidance to the
cuopt-multi-objective-explorationskill: the dual on a swept ε-constraint is the local slope of the Pareto frontier — the exchange rate between the objectives, read off each LP/QP solve — so the agent can report the tradeoff rate, and spot where to refine the sweep, without extra solves. Scoped to LP/QP off linear ε-constraints (MILP and quadratic-constraint problems return no duals). Adds a QP risk-return eval and clarifies the existing MILP eval to estimate the rate by differencing.Follows #1393 (per-type dual/sensitivity); companions #1407 (formulation) and #1408 (API skills). Verified in source and empirically on a 26.08 nightly (linear-constrained QP returns the expected dual; a quadratic constraint NaN-fills all duals).
validate_skills.shpasses;BENCHMARK.md/ skill card / signature regenerate via NVSkills-Eval.Checklist