Adv2 Framework: Expert Policy Orchestration

• Adv2 framework is a reinforcement learning paradigm that dynamically orchestrates expert policies using advantage-based weight updates, optimizing online matching problems.
• It employs a neural actor-critic architecture to scale across high-dimensional states and yield interpretable, convex mixtures of expert heuristics.
• The framework offers rigorous theoretical regret bounds and practical performance, as demonstrated by superior outcomes in organ exchange simulations.

The Adv2 framework is a reinforcement learning (RL) paradigm for expert policy orchestration in online matching problems. It formulates the selection and aggregation of expert policies through advantage-based weight updates, enabling adaptive, data-driven decision-making across diverse and high-dimensional system states. Adv2 is grounded in adversarial expert aggregation, facilitating reliable learning from biased value estimates while providing both theoretical regret guarantees and practical scalability through neural architectures.

1. Conceptual Foundations and Motivation

Adv2 addresses the limitations of static or myopic matching heuristics in complex, non-stationary environments such as organ exchange platforms and online marketplaces. Traditional heuristics are often interpretable but confined to particular regimes, resulting in decreased efficiency when operating conditions shift. Adv2 leverages a set of interpretable expert policies (e.g., "match the longest," "greedy max-payoff") and learns to orchestrate them by dynamically assigning state-dependent weights.

The orchestration relies on the estimated advantage function, which measures the incremental benefit of selecting a particular expert policy in a given state, relative to the current mixture of experts. This advantage-driven aggregation allows the framework to adaptively combine and reweight experts as system dynamics evolve, thus optimizing global performance over time.

2. Advantage-Based Weight Updates

The core operational mechanism in Adv2 is the advantage-based update of mixture weights for expert policies. Let $\{\pi_1, \dots, \pi_K\}$ denote $K$ expert policies. Given a state $s$, the mixture policy assigns weights $q_t(k|s)$ to each expert $k$. The update rule is:

$$q_t(k \mid s) = \frac{ \phi_t \left( \sum_{h=1}^{t-1} \mathcal{A}_{q_h \Pi}(s, k) \right) }{ \sum_{j \in [K]} \phi_t \left( \sum_{h=1}^{t-1} \mathcal{A}_{q_h \Pi}(s, j) \right) }$$

where $\phi_t$ is a potential function (typically exponential: $\phi_t(x) = \exp(\eta_t x)$), and $\mathcal{A}_{q_h \Pi}(s, k)$ is the estimated advantage of expert $k$ under the policy mixture at round $h$.

The practical implementation uses estimated advantages $\tilde{\mathcal{A}}_{q_t \Pi}(s, k)$ in place of true values, allowing operation under biased or noisy value estimates. This design generalizes to settings with only approximate value functions, critical for large-scale or partially observable systems.

3. Temporal-Difference Bias Bound and Value Estimation

Adv2's reliability hinges on the ability to estimate advantages accurately from temporal-difference (TD) learning algorithms, which can be biased under non-stationary or constant step-size settings. The framework introduces a finite-time bias bound:

$$| \mathbb{E}[ \tilde{\mathcal{A}}_{\pi, \tau}(s, a) ] - \mathcal{A}_{\pi}(s, a) | \leq 2 \| \mathbb{E}[ b_{(\tau)} ] \|_{\infty} \leq (1-\kappa)^{\tau} \cdot 2 E \cdot \| \mathbb{E}[ b_{(0)} ] \|_{\infty}$$

where $$b_{(\tau)}(s, a) = \tilde{\mathcal{Q}}_{\pi, \tau}(s, a) - Q_{\pi}(s, a)$$, $\kappa$ is a contraction factor (determined by step-size and minimal stationary probability), and $E$ is an instance-dependent constant. This bound guarantees geometric contraction of estimation bias, even with constant learning rates. Consequently, advantage estimates used in policy weights become increasingly reliable over time, substantiating the theoretical guarantees of the orchestrated policy’s performance.

4. Neural Actor-Critic Architecture

To scale Adv2 to high-dimensional and dynamic environments, a neural actor-critic architecture is deployed. The critic network approximates $Q$-values or direct advantage functions for experts, receiving state features as input. Training uses TD updates, benefiting directly from the finite-time bias bound.

The actor network supersedes explicit tabular storage by learning a parametric mapping from states to the probability simplex over experts. This parametrization enables the actor to output mixture weights $q(k|s)$ for any observed state. Training aligns the actor’s outputs to the target distributions from advantage-based aggregation using losses such as cross-entropy or KL divergence.

This architecture yields scalability (no need for combinatorial tables), adaptability (generalization over unseen states), and interpretability (the mixture is always a convex combination of explicit expert heuristics).

5. Regret Guarantees and Theoretical Performance

Adv2 provides both expectation and high-probability regret bounds relative to the best convex combination of expert policies:

• Expectation control theorem:

$$V_{q^* \Pi}(s_0) - \frac{1}{T} \sum_{t=1}^T \mathbb{E}[V_{q_t \Pi}(s_0)] \leq \frac{\epsilon}{1-\gamma} + \frac{B_{T,K}}{(1-\gamma)^2 T}$$

where $\epsilon$ is the bias bound, $\gamma$ the discount factor, $B_{T,K}$ a sublinear regret term (typically $O(\sqrt{T \log K})$).

• High-probability control: An additional term of order $(2\ln(1/\delta))/((1-\gamma)^2\sqrt{T})$ for probability at least $1-\delta$.

These guarantees ensure that the orchestrated policy converges toward the best-in-class mixture, with cumulative suboptimality growing sublinearly as data accrues. In practical settings—e.g., organ exchange—this translates to rapid convergence and system-level efficiency exceeding both standalone heuristics and traditional RL methods.

6. Practical Application: Organ Exchange Scenario

Simulation studies demonstrate Adv2's efficacy in organ exchange models characterized by variable donor-recipient pools and rapidly changing operational constraints. The framework identifies high-reward expert policies, adapts weights in response to evolving subpopulations (e.g., blood type distributions, urgency levels), and achieves superior cumulative rewards and convergence rates.

Expert orchestration dynamically balances interpretable heuristics, enabling the system to outperform individual experts and non-orchestrated RL baselines. The actor-critic implementation facilitates large-scale deployment without loss of interpretability—critical in domains where transparency and auditability are required.

7. Context and Significance

Adv2 combines advantage-weighted policy aggregation, finite-time TD bias control, and neural network-based scalability, establishing a principled, generalizable methodology for online decision-making systems. Its theoretical and empirical results demonstrate robust improvements in combinatorial resource allocation, with rigorous bounds ensuring both reliability and adaptability. This suggests Adv2 is particularly suitable for applications demanding interpretability, scalability, and performance guarantees under uncertainty and nonstationarity.

A plausible implication is that future extensions may incorporate more sophisticated value estimation techniques, richer expert sets, and automated calibration of aggregation potentials. The adv2 paradigm thus contributes a formal, scalable framework for orchestrating expert decision-making in complex systems, bridging interpretable policy heuristics with adaptive RL mechanisms.