Batch Exploration in ML and Optimization

• Batch Exploration is a set of strategies that process instances in groups, reducing feedback latency and enabling parallel resource utilization.
• It balances efficiency and adaptivity by using batched sampling to lower per-sample overhead while sometimes compromising immediate response to new data.
• Its practical applications span hyperparameter tuning, clinical trials, and high-throughput experiments, necessitating novel algorithmic adaptations.

Batch exploration refers to a family of strategies, algorithmic patterns, and systems engineering principles that leverage processing or evaluation in groups (“batches”) rather than in a purely sequential or individually adaptive fashion. Batch exploration is central in domains where (a) evaluating or collecting single instances is expensive or slow, (b) feedback or communication incurs latency, or (c) parallel resources can be exploited. Across machine learning, optimization, reinforcement learning, bandit problems, and scientific data processing, batch exploration mediates the tradeoff between adaptivity (responding after every sample) and efficiency (grouping many actions for collective processing), with deep implications for sample complexity, diversity, robustness to noise, and throughput.

1. Fundamentals of Batch Exploration

At its core, batch exploration contrasts with sequential, fully adaptive methods by limiting the points where new information can change the course of future sampling or execution. In stochastic multi-armed bandits, this means deciding arm pulls in rounds rather than after every single arm reward (Tuynman et al., 3 Feb 2025). In Bayesian optimization, this entails selecting sets of query points for parallel evaluation before seeing the function values (González et al., 2015, Mia et al., 4 Apr 2025). In reinforcement learning, batch exploration involves policy improvement from a fixed dataset, with no further online exploration possible (Fujimoto et al., 2019, Zhou et al., 2023).

Batching is motivated by both practical and theoretical considerations:

• Parallelization: Enables simultaneous execution, critical in large-scale experiments, distributed computing, hyperparameter search, and high-throughput screening.
• Latency and Delayed Feedback: In clinical trials or cloud computation, outcome feedback may only be available at the end of an epoch or trial.
• Sample Efficiency and Overhead: Batch strategies often reduce wall-clock time or per-sample setup overhead but at the potential cost of slower learning or diminished adaptivity.

Formally, batch exploration augments the design of exploration policies, acquisition or scheduling functions, and stopping criteria, all subject to batching constraints that restrict the frequency of policy updates.

2. Batch Exploration in Bandit and Pure Exploration Problems

Batch exploration in bandit models has received rigorous treatment, especially in the context of fixed-confidence pure exploration. Here, the goal is to identify optimal arms or partition arms with fewest samples while controlling for the number of communication rounds ("batches") (Tuynman et al., 3 Feb 2025). The fundamental insights include:

• Lower Bounds: Any $\delta$-correct batch pure exploration algorithm with nearly optimal sample complexity (i.e., within a constant factor of the sequential lower bound $T^*(\bm\mu) \ln(1/\delta)$) must use at least $\Omega(\log T^*(\bm\mu)/T_\text{min})$ batches, where $T^*(\bm\mu)$ reflects the instance difficulty and $T_\text{min}$ a known minimal complexity.
• Upper Bounds and PET Algorithm: The "Phased Explore then Track" (PET) algorithm nearly matches this bound, adaptively shrinking high-confidence regions through uniform exploration batches followed by allocation using instance-optimal proportions. The algorithm stops based on a likelihood-ratio criterion evaluated after batches, achieving nearly optimal sample complexity with only logarithmic batch rounds.
• Instance-Dependence and Affinity: The necessity of logarithmic (in $T^*(\bm\mu)$) batching is instance-dependent; easier instances permit fewer batches. Theoretical properties such as "affinity" of the instance complexity under scaling help in designing efficient batching schedules.

This formalization clarifies that, in bandit settings, batching imposes a statistical penalty that is fundamentally controlled, but not eliminated, by algorithmic design.

3. Batch Exploration in Bayesian Optimization

In Bayesian optimization (BO), batch exploration is central for minimizing wall-clock time and leveraging parallel hardware or experimental platforms (González et al., 2015, Nguyen et al., 2018, Mia et al., 4 Apr 2025). Core principles include:

• Acquisition Functions for Batches: Standard acquisition strategies (e.g., Expected Improvement, UCB) are extended via local penalization (González et al., 2015) or geometric distance (Nguyen et al., 2018) to select batches of points without redundant sampling. Local penalization introduces "exclusion zones" around selected points based on a Lipschitz constant, computed as:

$\phi(x; x_j) = 1 - p(x \in B_{r(x_j)}(x_j) )$

with $r(x_j) = (M - f(x_j))/L$ and the penalty effectively "repels" batch candidates from already chosen points.

• Efficient Wrap-Loops: Instead of recomputing the surrogate GP posterior after every point, efficient "wrap-loops" multiply the acquisition function by local penalizers iteratively to select consecutive batch points (González et al., 2015).
• Batch-Picking Methods: Strategies such as Local Penalization (LP), Kriging Believer (KB), and Constant Liar (CL) ensure that the batch is diversified.
• Problem Landscape and Noise Effects: The tractability of batch exploration and its noise sensitivity are highly problem-dependent: "needle-in-a-haystack" landscapes (Ackley) are much more susceptible to performance degradation from noise than smoother, multimodal problems (Hartmann) (Mia et al., 4 Apr 2025). Robust batch BO therefore requires careful surrogate modeling, batch selection, and acquisition hyperparameter tuning.
• Empirical Utility: Batch BO—when realized with principled batch acquisition and appropriate surrogate/variance estimation—achieves near-sequential sample efficiency and dramatically improves experimental throughput in applications such as high-throughput materials optimization and biological sequence design.

4. Batch and Mini-Batch Exploration in Stochastic Gradient and Neural Network Learning

In supervised learning—particularly in deep neural network training—mini-batch SGD and its batch size scaling present specific exploration-exploitation tradeoffs (Donmez et al., 2017, You et al., 2017):

• Cost-Fidelity Tradeoff: The EE-Grad framework models each mini-batch as an "oracle" with unknown variance-cost tradeoff, requiring sequential exploration–exploitation over batch sizes via upper-confidence bound (UCB) allocation. This empirical procedure nearly matches the optimal oracle (with negligible excess regret, $O(\ln T/T^2)$).
• Layerwise Adaptive Rate Scaling (LARS): In large-batch training for convolutional networks, LARS adaptively balances the learning rate for each layer based on weight and gradient norms, enabling stable training with batches up to 32K without loss of accuracy (You et al., 2017).
• Mode Collapse Mitigation: In settings such as reinforcement learning–based de novo molecular design, diverse mini-batch exploration via determinantal point processes (DPPs) acts as a principled repulsion mechanism, selecting batches that are explicitly diverse yet high-quality to mitigate collapse to few modes in the output space (Svensson et al., 26 Jun 2025).

These algorithmic contributions show that batch exploration is not a simple scaling of sequential techniques: explicit mechanisms for adaptivity, regularization, and diversity selection are necessary to avoid pitfalls associated with naively increasing batch size.

5. Batch Exploration in Reinforcement Learning and Offline/Batch RL

Batch exploration is particularly acute in reinforcement learning when exploration is no longer possible after collecting a fixed dataset ("batch RL" or "offline RL"). Key technical challenges and developments include:

• Extrapolation Error: Without the ability to interact with the environment, policies may select actions outside the support of the batch, leading to severe overestimation and policy degradation (Fujimoto et al., 2019, Zanette, 2020, Fakoor et al., 2021).
• Batch-Constrained and Safe Policy Algorithms: Techniques such as Batch-Constrained Q-learning (BCQ) restrict policy improvement only to actions with sufficient marginal probability under the behavior policy (Fujimoto et al., 2019, Kim et al., 2023), while methods like Continuous Doubly Constrained (CDC) Batch RL combine value- and policy-constraints to tightly regularize policy deviation and value overestimation (Fakoor et al., 2021).
• Hierarchical or Stackelberg Game-Theoretic Formulations: The StackelbergLearner algorithm formalizes the batch RL optimization as a leader-follower game, where the leader (policy) anticipates the response of the follower (critic/value function) and incorporates the total derivative of this hierarchical system, obtaining stronger local optimality and regret guarantees under weak coverage (Zhou et al., 2023):

$$DJ(\pi, q) = D_\pi J(\pi, q) - [D_{q, \pi} \mathcal{L}(\pi, q)]^\top (D^2_q \mathcal{L}(\pi, q))^{-1} D_q J(\pi, q)$$

• Safe Set Filtering and Conservative Evaluation: Recent work proposes to filter backups and policy evaluation to state–action pairs with sufficient batch support (using indicator $\zeta(s,a)$), thereby sidestepping the need for strong concentrability and avoiding overoptimism in unvisited regions (Liu et al., 2020). This yields error bounds that scale only with the coverage ratio constant rather than diverging with increasing mismatch between target and behavior policies.
• Exponential Sample Complexity Gaps: In infinite-horizon MDPs with linear function approximation, fundamental information-theoretic lower bounds show that offline RL with batch exploration, even under realizability and with the best possible coverage, requires an exponential number of distinct queries: $|\mu| \sim (1/(1-\gamma))^d$ for discount factor $\gamma$ and feature dimension $d$ (Zanette, 2020). Online RL that adapts its sampling sequence can sharply reduce this complexity.
• Task-Relevance and Human-Guided Exploration: Batch exploration with explicit relevance guidance (e.g., using discriminators trained on human-provided images of important states) increases the coverage of task-relevant state regions (doubling frequency of interaction with target objects in robotics experiments) and demonstrably improves downstream offline RL task performance (Chen et al., 2020).

6. Empirical Implications and Applications

Batch exploration directly impacts the design and performance of algorithms and systems across domains:

• Scientific Database Querying: Systems such as LifeRaft maximize I/O sharing by batching queries with overlapping data partitions, leading to 2× throughput improvements in large-scale astronomical databases (0909.1760). An aging-aware prioritization prevents starvation of low-contention queries.
• Materials and Molecular Design: Batch Bayesian optimization with robust acquisition/diversity methods accelerates experimental design for high-dimensional material composition or molecular property landscapes, with application-specific adaptation to landscape shape and noise (Mia et al., 4 Apr 2025, Svensson et al., 26 Jun 2025).
• High-Throughput Biology: Hierarchical batch exploration via learned embeddings efficiently searches combinatorially large biological sequence spaces, reducing cumulative regret and wall-clock time for massive candidate sets (Myers et al., 2020).
• Clinical Trials and Marketing: Dynamic batch bandit learning, with only $O(\log\log(T/s_0))$ batches for $T$ rounds and $s_0$-sparse reward vectors, achieves minimax optimal regret rates by leveraging LASSO estimation in high dimension (Ren et al., 2020).

The overarching lesson is that batch exploration unlocks practical scalability in settings where parallelism, latency, or cost make traditional adaptivity infeasible, but necessitates careful algorithmic innovation to avoid inefficiencies, degeneracies, or statistical inefficiency.

7. Open Directions and Theoretical Limits

Research on batch exploration has identified a number of open directions and fundamental limits:

• Batch Complexity–Sample Complexity Tradeoff: Optimal batching requires a calibrated balance between rounds of adaptation and total sample complexity; batch lower bounds are often instance-dependent, and practical scheduling must account for problem geometry and noise characteristics (Tuynman et al., 3 Feb 2025).
• Diversity and Mode Collapse: Especially in generative RL and scientific discovery, robust batch exploration must guarantee both sample quality and sufficient diversity—often necessitating explicit mechanisms such as DPP sampling (Svensson et al., 26 Jun 2025).
• Extrapolation and Distribution Shift: In offline RL, batch exploration is fundamentally constrained by coverage; techniques that regularize, filter, or hierarchically structure policy update are under active paper, with no single universally robust solution (Zhou et al., 2023, Fakoor et al., 2021).
• Algorithmic Scalability and Real-World Utility: Potential improvements include scalable approximate DPP sampling, adaptive batch sizing, dataset-aware surrogate/reward design, and automated selection of landscape- and noise-optimal batch selection policies.

The field is converging on a nuanced view: while batch exploration confers critical practical gains for realistic large-scale machine learning, optimization, and discovery, its statistical and algorithmic foundations require continual refinement to meet rising demands for robustness, adaptivity, and interpretability.