🤖 AI Summary
This study addresses the lack of empirical evidence for optimal execution in automated market makers (AMMs) under dynamic trading fees. The authors propose a closed-loop simulator grounded in equilibrium theory, incorporating constant-product liquidity pools with dynamic fees, fee-sensitive noise trading flows, and an analytical arbitrage mechanism, thereby enabling counterfactual analysis in a controlled environment. Using deep Q-networks (DQN), they compare reinforcement learning against multiple benchmark strategies and find that DQN significantly outperforms traditional scheduling and planning methods only in dynamic-fee settings. Across 1,000 held-out random seeds, DQN consistently reduces execution shortfall across all order sequencing configurations, achieving a 13.3 basis point improvement in the agent-last setting, while showing no significant advantage under constant fees.
📝 Abstract
Trader-facing dynamic fees are increasingly proposed for automated market makers (AMMs), but historical data do not identify how order flow would respond: trader-facing fees do not vary, trader types are latent, and a replayed tape is not a sequential decision environment. We therefore construct a minimal closed-loop simulator in which the missing signal exists by construction: two constant-product pools repriced by an equilibrium-inspired dynamic-fee rule, fee-sensitive noise flow, and closed-form CEX--AMM arbitrage. Equilibrium is used as a closure principle, not as an object the trader learns. Against a tuned benchmark ladder of schedule, planning, lookahead, and tabular policies, a small DQN is the only evaluated valid policy whose paired improvement over tuned one-step routing excludes zero. On a reserved final block of 1{,}000 seeds with completion forced to 1.0 for every policy, it reduces implementation shortfall under every tested intra-step ordering, by $13.3\bps$ of order notional under the pre-specified agent-last ordering, and the edge is concentrated in, and learned from, dynamic-fee environments: under constant fees the paired difference is indistinguishable from zero. The result is model-conditioned counterfactual evidence about execution control in AMMs, not evidence about historical traders, equilibrium play, or deployable profit.