A Learning-Based Hybrid Decision Framework for Matching Systems with User Departure Detection

Dynamic matching markets require decisions about whom to match and when: matching now yields value but removes participants who may create better future opportunities. We develop a value-based reinforcement-learning framework for this problem on finite, evolving weighted graphs. We study an infinite-horizon continuous-time model with stochastic arrivals, node-type transitions, edge realizations, and exogenous exits. We prove an event-time reduction: without loss of optimality, the planner acts immediately after each exogenous event and then waits for the next one. We further show that the optimal edge-wise $Q$-function is characterized by a single continuation-value function on post-decision residual graphs, reducing the learned object from state-action values to graph values. Exact action selection still requires combinatorial matching optimization; we approximate the value with a graph neural network, train it by temporal-difference learning, and use it in a forward-greedy matching heuristic. In a binary-type benchmark, the learned policy substantially outperforms immediate and threshold-greedy rules by preserving common nodes for rare arrivals of valuable matches while forming lower-value matches only in thick pools. In a kidney paired donation benchmark, it performs similarly to immediate greedy when exits are unpredictable, recovers the logic of patient matching when warnings are reliable, and outperforms the better of Immediate Greedy and Patient Greedy across intermediate warning probabilities. These results show that residual-graph value learning yields state-dependent dynamic matching policies that adapt to realized connectivity and exit information.

Two-sided matching markets often involve information that unfolds over time through interviews, repeated interaction, learning, and separation. Existing matching models typically reduce this process to immediate sub-Gaussian feedback about fixed preferences, missing settings where payoff-relevant information is revealed gradually and changes future matching decisions. We introduce a framework with temporally extended feedback, that formulates two-sided matching as a partially observable Markov game with costly pre-match screening, noisy post-match observations, evolving latent profiles, and endogenous continuation or dissolution. We instantiate this framework in Learn2Match, a multi-agent reinforcement-learning benchmark for dynamic matching markets. Learn2Match supports decentralized decision making over whom to interview, whom to match with, and when to dissolve a match, while evaluating policies using regret, social welfare, and an information-friction loss that measures the welfare gap caused by incomplete revelation of latent preferences. We find that independent PPO achieves higher cumulative social welfare and lower cumulative regret than the bandit-style CA-ETC baseline under temporally extended feedback, demonstrating the promise of MARL for dynamic matching markets. However, PPO still incurs higher information-friction loss, revealing that end-to-end MARL does not yet provide the coordinated exploration structure of matching-bandit methods. These results position Learn2Match as a benchmark for developing the next generation of matching-market algorithms: methods that are adaptive like RL agents, statistically disciplined like bandit algorithms, and structurally aware like stable-matching mechanisms. Please refer to https://sites.google.com/view/learn-to-match/home for the official website and the code link.

Matching repair after utility changes can reuse valid observations, but new evaluations must respect matching capacity and may return out of order. We study announced invalidations with bounded, possibly reward-dependent reporting delays and pending evaluations that do not occupy future matching capacity. Residualload repair (RLR) combines sound outcome certificates with batched matching schedules for unequal sample deficits. Its complete dyadic quota schedule admits a sharp issue-round bound with coefficient cb < 1.607 relative to the terminal residual endpoint load, together with separate delay and evidence-lifetime bounds. RLR-P monitors complete issue-order prefixes without changing the sampling plan before acceptance. With a deterministic pure oracle, a single-repair coupling from the same drained initial state guarantees no increase in certification time, issued observations, or time to a reusable checkpoint. We also derive an information-load lower bound. On fixed priority-star markets with unknown Bernoulli gaps, PrioritySearch attains the history-adjusted first-order constant for expected certification time as δ {\sim} 0, under hypothesis-independent linear history scaling and sublogarithmic reporting delays. Paired simulations and measured-feedback replay quantify the trade-offs: in the replay, RLR-P has lower mean capped update-certification time than a monitored width-based baseline, at higher oracle CPU cost.