---
title: Dynamic Batching Algorithms
url: https://www.emergentmind.com/topics/dynamic-batching-algorithm
type: topic
---

# Dynamic Batching Algorithms

Dynamic batching algorithms comprise a class of techniques that automatically group computations, requests, or data items into batches at runtime, with batch sizes and groupings determined adaptively based on workload characteristics, hardware constraints, efficiency objectives, or latency requirements. Unlike static batching, which uses pre-set batch sizes or batch composition, dynamic batching algorithms leverage runtime information and models (queuing, learning, memory usage, graph structure, etc.) to optimize the trade-off between efficiency, resource utilization, and responsiveness across a range of domains including neural network execution, distributed training, GPU inference serving, and dynamic graph algorithms.

## 1. Foundational Principles and Models

Dynamic batching leverages runtime adaptivity to maximize parallel hardware utilization while minimizing excess latency and resource waste. In neural network frameworks, dynamic batching groups isomorphic (structurally compatible) operations or subgraphs from variable input instances and fuses them into batched executions, reducing compute overhead and kernel launches compared to naïve instance-by-instance scheduling [1705.07860], [1904.07421], [1702.02181], [2302.03851]. For service queues and batch processing systems, policy optimization may be formalized as a semi-Markov decision process (SMDP) minimizing average latency and resource cost, yielding near-threshold or control-limit policies for dispatching batches [2501.02181].

Fundamental modeling elements include:
- Batch-dependent processing time: Service time and energy consumption depend on batch size, requiring intricate scheduling.
- Memory and resource constraints: Batching must prevent memory overflow and excessive per-batch resource utilization, with explicit memory models (e.g., for attention KV-cache size) guiding real-time batch size limits [2503.05248], [2507.17120].
- Latency-service level objectives (SLOs): Online serving systems integrate latency feedback to modulate batch sizes dynamically, balancing throughput against deadline compliance.
- Dynamic input structure: Batched execution must handle variable-length sequences, tree- or graph-shaped inputs, or evolving graphs whose topology changes across instances or time.

## 2. Algorithmic Frameworks for Dynamic Batching

Several architectural frameworks have emerged for dynamic batching:

**A. Neural Network Execution on Dynamic Graphs**
- Agenda-based scheduling (DyNet): Build a per-batch graph, partition nodes by operation signature, and use a greedy agenda algorithm to maximize batching opportunities at each topological depth [1705.07860].
- Just-in-time compilation (MXNet Gluon): Extend imperative API with delayed NDArrayFutures, group isomorphic operators or subgraphs during a defined batching scope, and memoize batched graphs for re-use [1904.07421].
- Finite state machine learning (ED-Batch): Learn an FSM-based scheduling policy via RL to minimize kernel launches, and use PQ-tree based memory planning to optimally layout batched data, reducing memory movement [2302.03851].

**B. Service Queue and Generic Batch Scheduling**
- SMDP-based dynamic batching formulates batch scheduling as a continuous-time decision process with the objective (weighted sum of response time and power) solved via truncated state-space DT-MDP and relative value iteration; tail-aggregation via abstract cost dramatically reduces state/time complexity [2501.02181].
- Latency/memory-aware online batch selection: At each scheduling epoch, compute batch size bound by memory model and by recent latency feedback, select the minimum to ensure SLA and avoid OOM [2503.05248].

**C. LLM Inference Serving**
- Bucket-based batching: Partition requests by sequence length into buckets minimizing padding waste; adaptively split/merge buckets according to observed load, and select real-time batch size via KV-cache memory model [2507.17120].
- Priority-aware scheduling: Enforce FCFS, SJF, or LJF policies within and across buckets to optimize latency or tokens/sec, with continuous batching at the decoding phase.

**D. Distributed and Heterogeneous Training**
- PID-based mini-batch controllers: Each worker in a heterogeneous cluster adjusts its mini-batch size according to proportional control on iteration time deviation from target; gradients are weighted proportionally to batch size for correctness [2305.12213].

## 3. Mathematical Formulations and Cost Models

Dynamic batching is rigorously modeled using:
- Cost and throughput models balancing batch size vs. processing/latency overheads, e.g., \( \text{TotalTime}(G) = T_{\text{analysis}}(G) + \alpha\,N_{\text{ops}}/B_{\text{eff}}(G) \) [1904.07421].
- SMDP and DT-MDP Bellman equations for service systems: optimal policy achieves \( h(s) = \min_a\{ c(s,a) - g^* y(s,a) + \sum_j m(j|s,a) h(j) \} \) [2501.02181].
- Memory-aware batch limiting is determined by \( N_{\text{max}} \leq M_{\text{safe}} / (2 L H D B) \) or probabilistic bounds via CLT and normal quantiles [2503.05248], [2507.17120].
- PID dynamic control for distributed batch sizing: \( b_k^{t+1} = b_k^t - X_k (T_k^t - T^*) \) where \( X_k \) is the throughput [2305.12213].

## 4. Implementation Strategies and Heuristics

Practical dynamic batching implementations integrate:
- Subgraph or operation signature hashing for grouping nodes.
- Heuristics to divide batching at subgraph, operator, or kernel granularity for trade-offs between matching cost and batch effectiveness [1904.07421].
- Caching and memoization of compiled batched graphs to avoid repeated scheduling analysis [1904.07421].
- Adaptive bucket formation and splitting algorithms, e.g. 50% midpoint rule and merging if total load drops below memory threshold [2507.17120].
- Deadbanding for PID controllers, bounds on per-worker batch size, EWMA smoothing over iteration times to avoid instability [2305.12213].
- Priority queues and PQ-tree-based memory planning to enforce alignment and minimize data movement [2302.03851].

## 5. Empirical Performance and Complexity Results

Significant empirical findings include:
- Neural dynamic batching achieves up to 6.25× speedup vs. manual or naïve per-instance execution; kernel launches reduced from millions to thousands per epoch [1904.07421], [1705.07860].
- ED-Batch improves throughput by 1.15× (chains), 1.39× (trees), and 2.45× (lattices) over state-of-the-art frameworks with RL-discovered policies, and memory PQ-tree planning reduces data movement up to 66× [2302.03851].
- LLM serving with BucketServe: up to 3.58× throughput improvement over UELLM, 1.93× higher request load under 80% SLO, 1.975× higher system capacity [2507.17120].
- SMDP-based policies enable up to 98% time and 63.5% state space reduction via abstract cost for tail state handling; consistently achieve Pareto-optimal trade-off curves (latency vs. energy) outperforming static and greedy baselines [2501.02181].
- Dynamic per-worker batching in heterogeneous training yields up to 4× speedup in wall-clock time compared to static, with improved accuracy in asynchronous SGD via reduced gradient staleness [2305.12213].
- For GNN batching, dynamic algorithms (JAX/Jraph) provide up to 2.7× speedup on CPU, but static batching may outperform on GPU for long runs with large batch sizes; no effect on model convergence or accuracy [2502.00944].

## 6. Limitations and Practical Guidelines

Known limitations and guidance include:
- Overhead: dynamic batching incurs matching/grouping, stacking/slicing, and queue management costs; overhead grows with structural heterogeneity and batch size [1705.07860], [2302.03851].
- Unique graphs: if every graph/sample is distinct, batching offers little benefit but can still incur analysis cost [1904.07421].
- Conditional control flow, cycles, and recursion are more challenging. Program-counter autobatching handles recursive allocation at higher memory overhead [1910.11141].
- Padding waste: bucket-based and dynamic batching strategies minimize but cannot eliminate padding in LLM and graph-serving workloads [2507.17120], [2502.00944].
- For distributed training, per-worker batch adjustment must avoid rapid oscillations ("ping-ponging"); use deadband and bounded updates [2305.12213].
- Dynamic batching only parallelizes operations with aligned signatures; deep, unbalanced structures may limit batching opportunity [1702.02181].

Best practices:
- Wrap repeated operations in sub-blocks for coarse batching [1904.07421].
- Scope dynamic batching tightly to batch-aligned computations, excluding logging/metrics [1705.07860].
- Pre-declare types and operation signatures; batch over depth or other partition axes [1702.02181].
- For variable GPU memory or latency constraints, continuously monitor running statistics and adapt batch size in real time, applying stricter bounds when traffic or resource spikes are observed [2503.05248], [2507.17120].

## 7. Impact and Future Directions

Dynamic batching algorithms have become foundational in high-performance neural network systems (MXNet, DyNet, TensorFlow Fold, vLLM, distributed ML frameworks), enabling efficient execution of models with irregular or dynamic computation graphs in both training and inference. The techniques bridge the gap between manual operator grouping and fully automated scheduling under complex constraints. Future research directions include:
- Extending RL- or SMDP-based policy discovery to more complex service queues and multi-stage systems.
- Integrating fine-grained batching with conditional computation and data-dependent control flow.
- Exploiting probabilistic knowledge of workload for tighter batch-sizing under SLA and memory constraints.
- Adapting bucket-based batching and memory feedback for emerging hardware with highly variable resource profiles.
- Pushing batch-dynamic algorithms into streaming, out-of-core, and cross-cluster environments.

Dynamic batching stands as a core abstraction for scalable, resource-efficient, and responsive computation systems, with continuing evolution toward unified, learning-based scheduling and integration across frameworks and hardware platforms [2507.17120], [2503.05248], [2302.03851], [1904.07421], [2501.02181], [2305.12213], [1705.07860].

Source: https://www.emergentmind.com/topics/dynamic-batching-algorithm