Multi-Round Distributed Learning

Updated 15 November 2025

Multi-Round Distributed Learning is an iterative process where multiple agents perform local computations and coordinate via structured communication to collectively optimize models.
It encompasses diverse scheduling regimes—cyclic, synchronous, asynchronous, and token-based—that balance trade-offs in staleness, efficiency, and synchronization overhead.
The approach offers robust convergence guarantees, adaptive communication strategies, and privacy mechanisms applicable in federated optimization, Bayesian inference, and reinforcement learning.

A multi-round distributed learning procedure refers to any iterative algorithmic process wherein multiple agents (workers, nodes, or devices) repeatedly perform and coordinate local computational updates and message exchanges over a network, with the goal of collectively learning a model, inferring a hypothesis, or achieving joint optimization. Such procedures are foundational across federated optimization, distributed Bayesian inference, decentralized reinforcement learning, and multi-agent systems, especially under practical constraints including privacy, communication cost, adversarial robustness, or partial data access. This article presents a comprehensive review of the key constructs, scheduling regimes, round structure, theoretical properties, protocol classes, and empirical findings for multi-round distributed learning as formalized in recent literature.

1. Scheduling and Communication Regimes

Distributed learning procedures are characterized by the structuring of rounds into interleaved sequences of local computation and communication, which drive the global learning dynamics. Essential scheduling paradigms include:

Cyclic/Round-robin scheduling: Each agent (or a subset) acts as the “collector” or “leader” in turn, while others play roles such as “seniors” (exploit) or “juniors” (explore), as in the ROMA-iQSS procedure (Lin et al., 5 Apr 2024).
Synchronous global rounds: All agents advance in lockstep, synchronizing after each local computation epoch, prominent in distributed ADMM-type methods (Ren et al., 21 Aug 2025, Ren et al., 23 Jan 2025, Liu et al., 2016).
Asynchronous or event-driven schedules: Nodes update whenever sufficient local or neighbor information becomes available, as in asynchronous multi-task learning (Hong et al., 4 Oct 2024).
Token- or message-passing rounds: Random-walk and dissemination protocols structure rounds around the movement of information tokens, as seen in privacy-preserving learning (Tao et al., 2020).

Each scheduling regime is associated with specific communication patterns (broadcast, peer-to-peer, aggregation at server), trade-offs in staleness, and synchronization overhead.

2. Iterative Update Mechanisms and Model Families

At the core of every multi-round procedure is an iterative mechanism, typically combining:

Local statistical update: Each agent applies an estimator or optimizer to its private data (e.g., stochastic gradient, Bayesian belief update, value-function update).
Model averaging or aggregation: Agents (or a global server) merge local updates across the network, often via arithmetic mean, geometric mean, robust M-estimators, or consensus operators.
Consistency enforcement: Distributed constraints are incorporated via Lagrangian penalties (ADMM), consensus terms, or trace-norm regularization (multi-task relationships).

Examples:

Value-based RL: Round-robin agents update state–state value maps $Q_k(s,s')$ and maintain best-next-state selectors, with only collectors writing to local replay buffers (Lin et al., 5 Apr 2024).
Distributed ADMM variants: Local stochastic-gradient optimization of $f_i(x)$ for $\tau$ epochs, then communication of compressed model differentials, followed by dual variable updates (Ren et al., 21 Aug 2025, Ren et al., 23 Jan 2025).
Distributed Bayesian inference: Repeated rounds of consensus (geometric mean over neighbors' beliefs) and innovation (Bayesian update on latest sample), with non-asymptotic concentration guarantees (Nedić et al., 2016).
Partial-information Bayesian learning: Only a randomly chosen hypothesis component is communicated per round; missing beliefs are estimated by recursive normalization (Rao et al., 18 Nov 2024).

3. Consensus, Robustness, and Adaptive Communication

Consensus and aggregation mechanisms are central to the cohesion and performance of distributed learning. Options and their properties include:

Aggregation Scheme	Robustness	Efficiency
Arithmetic mean	Not robust	Statistically optimal (benign)
Median/trimmed mean	Robust ( $<50\%$ up. cont.)	High variance
MM-estimation (REF)	Robust ( $<50\%$ ), efficient	Requires M-step
CenteredClipping	Byzantine tolerance (known $\delta$ )	Low overhead

Adaptive communication: Techniques such as agent-specific weights based on gradient alignment (cf. diffusion federated learning (Georgatos et al., 2022)) reduce the influence of outlier/misaligned updates, crucial under data heterogeneity.
Robust multi-round protocols: To counteract Byzantine or adversarial agents, protocols implement attack-tolerant aggregation (e.g., CenteredClip (Gorbunov et al., 2021), robust diffusion (Vlaski et al., 2022)) ensuring no single update can shift the model far from the consensus.

4. Theoretical Guarantees: Convergence, Optimality, and Sample Complexity

Rigorous analysis of multi-round distributed procedures often yields finite-time or asymptotic guarantees:

Linear or geometric convergence: Provided strong convexity and smoothness conditions, multi-round ADMM and robust aggregation procedures achieve linear decay of optimality gap or consensus error, even under stochastic gradients and communication compression (Ren et al., 21 Aug 2025, Vlaski et al., 2022).
Sample complexity bounds: For distributed Bayesian and non-Bayesian learning, explicit non-asymptotic rates link the number of rounds, network topology (spectral gap), and minimum Kullback-Leibler divergence between hypotheses to the probability mass assigned to the true hypothesis (Nedić et al., 2016).
Diffusion and consensus bias: Two-timescale convergence (inner and outer updates) ensures steady-state error in parameter estimation can be tuned via scheduler rates and penalty parameters (Hong et al., 4 Oct 2024).
Regret and utility–privacy trade-offs: Privacy-preserving procedures achieve bounded regret (within $O(\delta)$ of optimal) under local differential privacy guarantees and sublinear communication, provided network and sample size thresholds are met (Tao et al., 2020).

5. Adaptivity, Partial Information, and Privacy Constraints

Contemporary distributed learning frameworks frequently relax assumptions of full information sharing and unrestricted communication:

Partial information: Agents may transmit a subset of belief coordinates per round (e.g., only one selected hypothesis), updating missing values via normalization or temporal smoothing. Under strong connectivity and hypothesis mixing, such schemes retain almost-sure consistency, albeit at reduced convergence rate (Rao et al., 18 Nov 2024).
Privacy mechanisms: Local differential privacy is ensured through randomized response and local perturbation of transmitted updates, with subsequent debiasing and normalization steps. Multi-round dissemination via random walks ensures near-uniform sampling across the network, crucial for learning utility (Tao et al., 2020).
Memory-efficient estimation: Reduced-memory protocols trade off a slight speed loss for a significant reduction in per-agent storage cost, as with neighbor belief estimation using local history rather than tracking all missed messages (Rao et al., 18 Nov 2024).

6. Empirical Validation and Practical Considerations

Empirical results across varied multi-round protocols show consistently:

Variance reduction via structured scheduling: Round-robin and ROMA-like schemes (as in ROMA-iQSS) sharply reduce outcome variance and episodes to convergence relative to synchronous or unstructured multi-agent interaction (Lin et al., 5 Apr 2024).
Communication-efficiency/accuracy trade-off: Increasing the number of local training steps per round reduces communication but may require tighter step-size control and impacts memory and computation (as shown in ADMM-type protocols (Ren et al., 21 Aug 2025, Ren et al., 23 Jan 2025)).
Robust aggregation: In high-dimensional and adversarial settings, REF-type MM-estimators or clipping ensure statistical efficiency and outlier tolerance; other schemes (median/trimmed mean) require near-total participation for comparable performance (Vlaski et al., 2022, Gorbunov et al., 2021).
Partial communication impact: Memory-saving partial-information sharing achieves almost-sure learning, but slows rejection of false hypotheses compared to full-information protocols (Rao et al., 18 Nov 2024).
Topology and heterogeneity: In non-i.i.d. or networked multi-task settings, adaptive weighting of information links and group-based schedule/penalties mitigate the effects of heterogeneity and topology-induced bias, leading to markedly improved convergence and accuracy (Georgatos et al., 2022, Hong et al., 4 Oct 2024).

7. Outlook and Extensions

Multi-round distributed learning has demonstrated flexibility and strong theoretical guarantees across a spectrum from federated optimization to collective Bayesian inference and reinforcement learning. Current lines of work explore:

Integration of advanced privacy (e.g., local/secure aggregation with differential privacy).
Continued reduction in per-round communication via model/gradient compression and partial information schemes.
Deeper robustness against complex adversarial models (Byzantine/general non-benign behaviors).
Extensions to asynchronous, event-driven, and innumerable-agent regimes, with scaling theory accounting for spectral gap, memory, and computational heterogeneity.

Papers analyzed underscore the principle that carefully architected round structure, scheduling, and aggregation—matched to network and statistical constraints—enables distributed systems to match, within constant factors, the learning efficiency and robustness of centralized counterparts.