{ "approach": { "idea": "Tune only pHat update trust on CH: first-in-step alpha x subsequent-retail alpha, followed by gap scaling at the best refined cell.", "reference": { "name": "CH", "code_sha256": "6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3", "mean_edge_seeds_0_999": 525.5258821780834, "requester_reference_mean_edge": 525.525882178, "reference_mean_matches_within_1e_6": true }, "grid": { "alpha": [ 0.18, 0.22, 0.27, 0.32 ], "retail": [ 0.03, 0.06, 0.09 ], "seed_start": 10000, "n_per_cell": 500 }, "refinement": { "anchor": "a27_r06", "cells": [ { "alpha": 0.25, "retail": 0.05 }, { "alpha": 0.25, "retail": 0.06 }, { "alpha": 0.25, "retail": 0.07 }, { "alpha": 0.27, "retail": 0.05 }, { "alpha": 0.27, "retail": 0.06 }, { "alpha": 0.27, "retail": 0.07 }, { "alpha": 0.29, "retail": 0.05 }, { "alpha": 0.29, "retail": 0.06 }, { "alpha": 0.29, "retail": 0.07 } ], "seed_start": 11000, "n_per_cell": 1000 }, "gap_scaling": "For firstInStep only: alpha *= min(trade.timestamp - lastTs, 4) / 2, computed in integer WAD arithmetic. Subsequent retail alpha is unchanged. Timestamp zero gives zero first-step alpha.", "selection": { "variant": "a27_r07", "code_sha256": "960548979be7b6d184f5bdbc0aa7a49e33e8a1621d0a53157335736f99a1aed1", "tuning_mean_diff": 0.001736044121273494, "tuning_se": 0.011693009597094963, "frozen_before_confirmation": true, "selection_rule": "Highest paired tuning mean among changed-parameter refinements and gap scaling; the identity CH control is excluded from final candidate selection.", "promotion_rule": "mean_diff > 2 * se on seeds 600000..601999, once; no holdout-based retuning.", "promote": false }, "measurement": "Each strategy is separately simulated against the fixed 30 bps normalizer using unmodified simulator commit 6b6921f8d463314aa7c96234e1be25a25245f704 and amm_sim_rs.run_batch. Configs reproduce MatchRunner._build_configs: numpy default_rng(seed) draws mean size U(19,21), arrival rate U(0.6,1.0), sigma U(0.000882,0.001008), in that order; 10000 steps, initial price/X/Y=100/100/10000, mu=0, dt=1, size_sigma=1.2, buy_prob=0.5. Rust price RNG uses seed; retail uses seed+1. Difference is candidate submission edge minus CH submission edge on the same seed. Standard errors use sample standard deviation (ddof=1)/sqrt(n). Worst means smallest signed paired difference. Chunks of 16, eight workers. No seeds 900000..909999 were used.", "validation": { "amm_match_validate": "Validating strategy...\nCompiling strategy...\nStrategy 'no_cubic' validated successfully!", "gas_stress": { "calls": 721, "after_initialize_gas": 185532, "max_after_swap_gas": 69575, "gas_limit": 250000, "all_success": true }, "unroll_equivalence": { "unrolling_identical_fee_pairs": 720, "original": { "calls": 721, "after_initialize_gas": 185532, "max_after_swap_gas": 69601, "gas_limit": 250000, "all_success": true }, "unrolled": { "calls": 721, "after_initialize_gas": 185532, "max_after_swap_gas": 69575, "gas_limit": 250000, "all_success": true } }, "storage_slots_used": "0..10 only", "loops": "None in delivered Strategy. Original bounded power loop was unrolled in refinements and final code; exact multiplication order retained for elapsed in 0..8, the only reachable range. This is a semantic-preserving change, not a second fee mechanism." }, "ranked_promotions": [], "limitations": "Local simulator evidence only; no official leaderboard submission. StarterStrategy was validated but no paired gain over StarterStrategy was measured in this item. Public write-up claims were not independently reproduced." }, "tried": [ { "variant": "a27_r06", "phase": "grid_500_original_bounded_power_helper", "alpha": 0.27, "retail": 0.06, "scaled": false, "seeds": "10000..10499", "n": 500, "mean_diff": 0.0, "se": 0.0, "code_sha256": "6dd68f77a70900319460215374143dbd5d924198450a46d9f5f91f6b1e3d35c3", "mean_edge": 523.6459153427178, "worst": [ { "seed": 10472, "diff": 0.0, "candidate_edge": 573.4141825579956, "reference_edge": 573.4141825579956 }, { "seed": 10473, "diff": 0.0, "candidate_edge": 568.1715057046089, "reference_edge": 568.1715057046089 }, { "seed": 10474, "diff": 0.0, "candidate_edge": 599.35186851571, "reference_edge": 599.35186851571 }, { "seed": 10475, "diff": 0.0, "candidate_edge": 781.2752665258633, "reference_edge": 781.2752665258633 }, { "seed": 10476, "diff": 0.0, "candidate_edge": 546.5877625244473, "reference_edge": 546.5877625244473 } ] }, { "variant": "a27_r03", "phase": "grid_500_original_bounded_power_helper", "alpha": 0.27, "retail": 0.03, "scaled": false, "seeds": "10000..10499", "n": 500, "mean_diff": -0.23682266473246863, "se": 0.04873443371742719, "code_sha256": "89e9432e7a41024fdf0d01de407bafd2fb4162d86aa5600ee5c48069f694336a", "mean_edge": 523.4090926779853, "worst": [ { "seed": 10014, "diff": -21.65364587528859, "candidate_edge": 560.766340044868, "reference_edge": 582.4199859201566 }, { "seed": 10006, "diff": -1.7760725527414252, "candidate_edge": 534.1069780994977, "reference_edge": 535.8830506522391 }, { "seed": 10359, "diff": -1.5683167407485712, "candidate_edge": 395.39321485346477, "reference_edge": 396.96153159421334 }, { "seed": 10095, "diff": -1.542671787790482, "candidate_edge": 570.4851303090678, "reference_edge": 572.0278020968583 }, { "seed": 10226, "diff": -1.4942332721348066, "candidate_edge": 572.401155058427, "reference_edge": 573.8953883305618 } ] }, { "variant": "a27_r09", "phase": "grid_500_original_bounded_power_helper", "alpha": 0.27, "retail": 0.09, "scaled": false, 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"reference_edge": 456.07889006149486 }, { "seed": 11983, "diff": -1.6938032081434358, "candidate_edge": 645.6720820002671, "reference_edge": 647.3658852084105 }, { "seed": 11564, "diff": -1.508268548296428, "candidate_edge": 554.4498087513741, "reference_edge": 555.9580772996705 }, { "seed": 11775, "diff": -1.445288227023923, "candidate_edge": 492.5100096366847, "reference_edge": 493.9552978637086 } ] }, { "variant": "a27_r07_gap", "phase": "elapsed_scaling_1000_unrolled_power_helper", "alpha": 0.27, "retail": 0.07, "scaled": true, "seeds": "11000..11999", "n": 1000, "mean_diff": -9.716887759044535, "se": 0.057515356935844635, "code_sha256": "8c77eca55b3dbc036a214b26ff674bef73fcac4afab91c09649a16145536e4c9", "mean_edge": 510.93355167202907, "worst": [ { "seed": 11910, "diff": -17.797547657275004, "candidate_edge": 622.9107796817312, "reference_edge": 640.7083273390062 }, { "seed": 11425, "diff": -15.978456562740462, "candidate_edge": 689.6859976396371, "reference_edge": 705.6644542023776 }, { "seed": 11998, "diff": -15.631905935851819, "candidate_edge": 640.2711305456472, "reference_edge": 655.903036481499 }, { "seed": 11387, "diff": -15.35975781547154, "candidate_edge": 622.9860023557237, "reference_edge": 638.3457601711953 }, { "seed": 11982, "diff": -15.18559707448594, "candidate_edge": 671.0089917448573, "reference_edge": 686.1945888193433 } ] } ], "next": "Retain CH as the best. This frozen candidate does not clear mean gain > twice its standard error on the fresh holdout; report the result without retuning on those seeds.", "code": "// SPDX-License-Identifier: MIT\npragma solidity ^0.8.24;\n\nimport {AMMStrategyBase} from \"./AMMStrategyBase.sol\";\nimport {TradeInfo} from \"./IAMMStrategy.sol\";\n\ncontract Strategy is AMMStrategyBase {\n uint256 constant ELAPSED_CAP = 8;\n uint256 constant SIGNAL_THRESHOLD = WAD / 650;\n uint256 constant DIR_DECAY = 750000000000000000;\n uint256 constant ACT_DECAY = 530000000000000000;\n uint256 constant SIZE_DECAY = 530000000000000000;\n uint256 constant TOX_DECAY = 910000000000000000;\n uint256 constant SIGMA_DECAY = 690000000000000000;\n uint256 constant LAMBDA_DECAY = 990000000000000000;\n uint256 constant SIZE_BLEND_DECAY = 828000000000000000;\n uint256 constant TOX_BLEND_DECAY = 51000000000000000;\n uint256 constant ACT_BLEND_DECAY = 985000000000000000;\n uint256 constant PHAT_ALPHA = 270000000000000000;\n uint256 constant PHAT_ALPHA_RETAIL = 70000000000000000;\n uint256 constant DIR_IMPACT_MULT = 4;\n uint256 constant GATE_SIGMA_MULT = 7200000000000000000;\n uint256 constant MIN_GATE = 30000000000000000;\n uint256 constant TRADE_TOX_BOOST = 3500 * BPS;\n uint256 constant STALE_ATTRACT_FRAC = 1050000000000000000;\n uint256 constant RET_CAP = WAD / 35;\n uint256 constant TOX_CAP = WAD / 5;\n uint256 constant TRADE_RATIO_CAP = WAD / 5;\n uint256 constant LAMBDA_CAP = 1820000000000000000;\n uint256 constant STEP_COUNT_CAP = 64;\n uint256 constant BASE_FEE = 4 * BPS;\n uint256 constant SIGMA_COEF = 200000000000000000;\n uint256 constant LAMBDA_COEF = 12 * BPS;\n uint256 constant FLOW_SIZE_COEF = 4842 * BPS;\n uint256 constant TOX_COEF = 300 * BPS;\n uint256 constant TOX_QUAD_COEF = 15000 * BPS;\n uint256 constant ACT_COEF = 91843 * BPS;\n uint256 constant DIR_COEF = 20 * BPS;\n uint256 constant DIR_TOX_COEF = 100 * BPS;\n uint256 constant STALE_DIR_COEF = 6850 * BPS;\n uint256 constant SIGMA_TOX_COEF = 500 * BPS;\n uint256 constant TAIL_KNEE = 600 * BPS;\n uint256 constant TAIL_SLOPE_PROTECT = 930000000000000000;\n uint256 constant TAIL_SLOPE_ATTRACT = 850000000000000000;\n\n function afterInitialize(uint256 initialX, uint256 initialY) external override returns (uint256, uint256) {\n slots[0] = BASE_FEE; slots[1] = BASE_FEE; slots[2] = 0; slots[3] = WAD; slots[4] = 0;\n slots[5] = initialX > 0 ? wdiv(initialY, initialX) : 100 * WAD;\n slots[6] = 950000000000000; slots[7] = 800000000000000000; slots[8] = 2000000000000000;\n slots[9] = 0; slots[10] = 0;\n return (BASE_FEE, BASE_FEE);\n }\n\n function afterSwap(TradeInfo calldata trade) external override returns (uint256, uint256) {\n uint256 prevBidFee = slots[0]; uint256 prevAskFee = slots[1]; uint256 lastTs = slots[2];\n uint256 dirState = slots[3]; uint256 actEma = slots[4]; uint256 pHat = slots[5];\n uint256 sigmaHat = slots[6]; uint256 lambdaHat = slots[7]; uint256 sizeHat = slots[8];\n uint256 toxEma = slots[9]; uint256 stepTradeCount = slots[10];\n\n bool isNewStep = trade.timestamp > lastTs;\n if (isNewStep) {\n uint256 elapsedRaw = trade.timestamp - lastTs;\n uint256 elapsed = elapsedRaw > ELAPSED_CAP ? ELAPSED_CAP : elapsedRaw;\n dirState = _decayCentered(dirState, DIR_DECAY, elapsed);\n actEma = wmul(actEma, _powWad(ACT_DECAY, elapsed));\n sizeHat = wmul(sizeHat, _powWad(SIZE_DECAY, elapsed));\n toxEma = wmul(toxEma, _powWad(TOX_DECAY, elapsed));\n if (stepTradeCount > 0 && elapsedRaw > 0) {\n uint256 lambdaInst = (stepTradeCount * WAD) / elapsedRaw;\n if (lambdaInst > LAMBDA_CAP) lambdaInst = LAMBDA_CAP;\n lambdaHat = wmul(lambdaHat, LAMBDA_DECAY) + wmul(lambdaInst, WAD - LAMBDA_DECAY);\n }\n stepTradeCount = 0;\n }\n\n bool firstInStep = stepTradeCount == 0;\n uint256 spot = trade.reserveX > 0 ? wdiv(trade.reserveY, trade.reserveX) : pHat;\n if (pHat == 0) pHat = spot;\n\n uint256 feeUsed = trade.isBuy ? prevBidFee : prevAskFee;\n uint256 gamma = feeUsed < WAD ? WAD - feeUsed : 0;\n uint256 pImplied;\n if (gamma == 0) { pImplied = spot; }\n else { pImplied = trade.isBuy ? wmul(spot, gamma) : wdiv(spot, gamma); }\n\n {\n uint256 ret = pHat > 0 ? wdiv(absDiff(pImplied, pHat), pHat) : 0;\n uint256 alpha = firstInStep ? PHAT_ALPHA : PHAT_ALPHA_RETAIL;\n uint256 adaptiveGate = wmul(sigmaHat, GATE_SIGMA_MULT);\n if (adaptiveGate < MIN_GATE) adaptiveGate = MIN_GATE;\n if (ret <= adaptiveGate) { pHat = wmul(pHat, WAD - alpha) + wmul(pImplied, alpha); }\n if (firstInStep) {\n if (ret > RET_CAP) ret = RET_CAP;\n sigmaHat = wmul(sigmaHat, SIGMA_DECAY) + wmul(ret, WAD - SIGMA_DECAY);\n }\n }\n\n uint256 tradeRatio = trade.reserveY > 0 ? wdiv(trade.amountY, trade.reserveY) : 0;\n if (tradeRatio > TRADE_RATIO_CAP) tradeRatio = TRADE_RATIO_CAP;\n\n if (tradeRatio > SIGNAL_THRESHOLD) {\n uint256 push = tradeRatio * DIR_IMPACT_MULT;\n if (push > WAD / 4) push = WAD / 4;\n if (trade.isBuy) {\n dirState = dirState + push;\n if (dirState > 2 * WAD) dirState = 2 * WAD;\n } else {\n dirState = dirState > push ? dirState - push : 0;\n }\n actEma = wmul(actEma, ACT_BLEND_DECAY) + wmul(tradeRatio, WAD - ACT_BLEND_DECAY);\n sizeHat = wmul(sizeHat, SIZE_BLEND_DECAY) + wmul(tradeRatio, WAD - SIZE_BLEND_DECAY);\n if (sizeHat > WAD) sizeHat = WAD;\n }\n\n uint256 tox = pHat > 0 ? wdiv(absDiff(spot, pHat), pHat) : 0;\n if (tox > TOX_CAP) tox = TOX_CAP;\n toxEma = wmul(toxEma, TOX_BLEND_DECAY) + wmul(tox, WAD - TOX_BLEND_DECAY);\n uint256 toxSignal = toxEma;\n\n stepTradeCount = stepTradeCount + 1;\n if (stepTradeCount > STEP_COUNT_CAP) stepTradeCount = STEP_COUNT_CAP;\n\n uint256 flowSize = wmul(lambdaHat, sizeHat);\n uint256 fBase = BASE_FEE + wmul(SIGMA_COEF, sigmaHat) + wmul(LAMBDA_COEF, lambdaHat) + wmul(FLOW_SIZE_COEF, flowSize);\n uint256 fMid = fBase + wmul(TOX_COEF, toxSignal) + wmul(TOX_QUAD_COEF, wmul(toxSignal, toxSignal)) + wmul(ACT_COEF, actEma);\n fMid = fMid + wmul(SIGMA_TOX_COEF, wmul(sigmaHat, toxSignal));\n\n uint256 dirDev; bool sellPressure;\n if (dirState >= WAD) { dirDev = dirState - WAD; sellPressure = true; }\n else { dirDev = WAD - dirState; sellPressure = false; }\n\n uint256 skew = wmul(DIR_COEF, dirDev) + wmul(DIR_TOX_COEF, wmul(dirDev, toxSignal));\n uint256 bidFee; uint256 askFee;\n if (sellPressure) {\n bidFee = fMid + skew;\n askFee = fMid > skew ? fMid - skew : 0;\n } else {\n askFee = fMid + skew;\n bidFee = fMid > skew ? fMid - skew : 0;\n }\n\n {\n uint256 staleShift = wmul(STALE_DIR_COEF, toxSignal);\n uint256 attractShift = wmul(staleShift, STALE_ATTRACT_FRAC);\n if (spot >= pHat) {\n bidFee = bidFee + staleShift;\n askFee = askFee > attractShift ? askFee - attractShift : 0;\n } else {\n askFee = askFee + staleShift;\n bidFee = bidFee > attractShift ? bidFee - attractShift : 0;\n }\n }\n\n {\n bool tradeAligned = (trade.isBuy && spot >= pHat) || (!trade.isBuy && spot < pHat);\n if (tradeAligned) {\n uint256 tradeBoost = wmul(TRADE_TOX_BOOST, tradeRatio);\n if (trade.isBuy) { bidFee = bidFee + tradeBoost; }\n else { askFee = askFee + tradeBoost; }\n }\n }\n\n if (sellPressure) {\n bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_PROTECT));\n askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_ATTRACT));\n } else {\n askFee = clampFee(_compressTailWithSlope(askFee, TAIL_SLOPE_PROTECT));\n bidFee = clampFee(_compressTailWithSlope(bidFee, TAIL_SLOPE_ATTRACT));\n }\n\n slots[0] = bidFee; slots[1] = askFee; slots[2] = trade.timestamp;\n slots[3] = dirState; slots[4] = actEma; slots[5] = pHat;\n slots[6] = sigmaHat; slots[7] = lambdaHat; slots[8] = sizeHat;\n slots[9] = toxEma; slots[10] = stepTradeCount;\n\n return (bidFee, askFee);\n }\n\n function _compressTailWithSlope(uint256 fee, uint256 slope) internal pure returns (uint256) {\n if (fee <= TAIL_KNEE) return fee;\n return TAIL_KNEE + wmul(fee - TAIL_KNEE, slope);\n }\n\n function _powWad(uint256 factor, uint256 exp) internal pure returns (uint256 result) {\n result = WAD;\n if (exp & 1 == 1) result = wmul(result, factor);\n factor = wmul(factor, factor);\n if (exp & 2 == 2) result = wmul(result, factor);\n factor = wmul(factor, factor);\n if (exp & 4 == 4) result = wmul(result, factor);\n factor = wmul(factor, factor);\n if (exp & 8 == 8) result = wmul(result, factor);\n }\n\n function _decayCentered(uint256 centered, uint256 decayFactor, uint256 elapsed) internal pure returns (uint256) {\n uint256 mul = _powWad(decayFactor, elapsed);\n if (centered >= WAD) { return WAD + wmul(centered - WAD, mul); }\n uint256 below = wmul(WAD - centered, mul);\n return below < WAD ? WAD - below : 0;\n }\n\n function getName() external pure override returns (string memory) { return \"no_cubic\"; }\n}\n", "code_sha256": "960548979be7b6d184f5bdbc0aa7a49e33e8a1621d0a53157335736f99a1aed1", "delta": "@@ -20 +20 @@\n- uint256 constant PHAT_ALPHA_RETAIL = 60000000000000000;\n+ uint256 constant PHAT_ALPHA_RETAIL = 70000000000000000;\n@@ -186,5 +186,7 @@\n- while (exp > 0) {\n- if (exp & 1 == 1) result = wmul(result, factor);\n- factor = wmul(factor, factor);\n- exp >>= 1;\n- }\n+ if (exp & 1 == 1) result = wmul(result, factor);\n+ factor = wmul(factor, factor);\n+ if (exp & 2 == 2) result = wmul(result, factor);\n+ factor = wmul(factor, factor);\n+ if (exp & 4 == 4) result = wmul(result, factor);\n+ factor = wmul(factor, factor);\n+ if (exp & 8 == 8) result = wmul(result, factor);", "score": { "seed_start": 0, "n": 1000, "mean_edge": 525.503052204802, "se": 2.7889180186891607 }, "paired": { "reference": "CH 6dd68f77", "seed_start": 600000, "n": 2000, "mean_diff": -0.011316405044711786, "se": 0.007172340403675725, "worst": [ { "seed": 600151, "diff": -1.8578441623375284, "candidate_edge": 605.7775381575341, "reference_edge": 607.6353823198716 }, { "seed": 601289, "diff": -1.6110271649774859, "candidate_edge": 650.9138479894913, "reference_edge": 652.5248751544688 }, { "seed": 601782, "diff": -1.340362910596241, "candidate_edge": 780.085545358853, "reference_edge": 781.4259082694492 }, { "seed": 601802, "diff": -1.2398879021545213, "candidate_edge": 454.47121607222306, "reference_edge": 455.7111039743776 }, { "seed": 601613, "diff": -1.2187646874406255, "candidate_edge": 473.8335433017073, "reference_edge": 475.05230798914795 } ] }, "seconds_per_simulation": 0.20011658265208826, "validate_ok": true, "blocked": null, "citations": { "measurement_sources": [ "https://raw.githubusercontent.com/ChengHua926/amm-challenge/d34a5199c59a4c44d5336a25f1436b4ae1f21104/contracts/src/Strategy.sol", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/match.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_competition/competition/config.py", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/simulation/engine.rs", "https://raw.githubusercontent.com/benedictbrady/amm-challenge/6b6921f8d463314aa7c96234e1be25a25245f704/amm_sim_rs/src/evm/strategy.rs" ], "public_writeups": [ { "url": "https://raw.githubusercontent.com/jiayaoqijia/amm-challenge-yq/3e9dc7d5a6192c88b562a0f8d9c172ca566ec94d/README.md", "finding": "YQ documents a sigma-gated pHat filter and first-in-step alpha 0.26." }, { "url": "https://raw.githubusercontent.com/dipankar/amm-challenge/c588ae6c47fc9af2063c9bb1f2efbeb0dd276dab/ANALYSIS.md", "finding": "Dipankar describes first/subsequent alpha 0.26/0.05 and emphasizes state estimation." }, { "url": "https://medium.com/@crypto_algebra/amm-fee-challenge-notes-from-our-run-on-optimization-arena-4e980dbbd699", "finding": "Algebra discusses first-trade block ordering, probabilistic estimates, and asymmetric fees. Read through the web reader; direct HTTP fetch returned 403." } ], "timing_definition": "Wall time for the final candidate confirmation run divided by 2000 individual simulations; includes per-seed edge extraction, excludes compilation and config construction. Parallel throughput, not CPU time." } }