In this paper, the causal bandit problem is investigated, with the objective of maximizing the long-term reward by selecting an optimal sequence of interventions on nodes in an unknown causal graph. It is assumed that both the causal topology and the distribution of interventions are unknown. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed. Numerical results suggest that this method has a much lower sample complexity relative to the prior art by learning sub-graphs. However, we note that a sample complexity analysis for the new algorithm has not been undertaken, as of yet. Under the assumption of minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound-based intervention selection to optimize the reward. Further, we consider a particular instance of non-stationary bandits wherein both the causal topology and interventional distributions can change. Our solution is the design of a sub-graph change detection mechanism that requires a modest number of samples. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in stationary and nonstationary settings. Averaged over 100 randomly generated causal bandits, the proposed scheme takes significantly fewer samples to learn the causal structure and achieves a reward gain of 85% compared to existing approaches.

The proliferation of large language model (LLM) agents has enabled increasingly complex multi-step automation; however, composing multiple agents into coherent systems introduces significant orchestration challenges that remain poorly documented. This survey examines LLM-based multi-agent orchestration from 2023 through early 2026 (literature cutoff: March 2026), with explicit attention to the evidence hierarchy used to interpret deployment claims. We propose a three-topology, one-adaptivity taxonomy—centralized, decentralized, and hierarchical coordination topologies, each optionally augmented with a dynamic–adaptive control axis—grounded in classical multi-agent systems theory and recent empirical evidence. We compare six leading frameworks (LangGraph, CrewAI, AutoGen/Microsoft Agent Framework, OpenAI Agents SDK, MetaGPT, and DSPy) along axes directly relevant to practitioners: state-management granularity, token-cost structure, failure-recovery options, and design philosophy. The emerging protocol stack is examined in terms of why MCP (agent-to-tool) and A2A (agent-to-agent) occupy complementary layers, how the ACP–A2A merger signals protocol convergence, and where ANP’s decentralized-discovery design fits. Production design considerations—state management, task planning, error handling, scalability, and security—are evaluated with reference to published benchmarks. Vendor-reported figures are marked † throughout and held to a documented evidence hierarchy, which separates them from peer-reviewed and government-evaluator measurements. We close by identifying eight open challenges and proposing a six-dimension evaluation framework for multi-agent coordination quality. This paper offers practitioners a decision framework covering taxonomy, framework selection, protocol adoption, and early operational pilots.

The proliferation of large language model (LLM) agents has enabled increasingly complex 2 multi-step automation; however, composing multiple agents into coherent systems intro3 duces significant orchestration challenges that remain poorly documented. This survey 4 examines LLM-based multi-agent orchestration from 2023 through early 2026 (literature 5 cutoff: March 2026). We propose a three-topology, one-adaptivity taxonomy—centralized, 6 decentralized, and hierarchical coordination topologies, each optionally augmented with 7 a dynamic/adaptive control axis—grounded in classical multi-agent systems theory and 8 recent empirical evidence. We compare four leading frameworks (LangGraph, CrewAI, 9 AutoGen/Microsoft Agent Framework, and OpenAI Agents SDK) along axes directly rele10 vant to practitioners: state-management granularity, token cost structure, failure-recovery 11 options, and design philosophy. The emerging protocol stack is examined in terms of why 12 MCP (agent-to-tool) and A2A (agent-to-agent) occupy complementary layers, how the 13 ACP–A2A merger signals protocol convergence, and where ANP’s decentralized-discovery 14 design fits. Production design considerations—state management, task planning, error 15 handling, scalability, and security—are evaluated with reference to published benchmarks. 16 We close by identifying five open challenges and proposing a six-dimension evaluation 17 framework for multi-agent coordination quality. This paper provides practitioners with 18 a decision framework spanning taxonomy, framework selection, protocol adoption, and 19 production deployment.

Stochastic Optimization is a cornerstone of operations research, providing a framework to solve optimization problems under uncertainty. Despite the development of numerous algorithms to tackle these problems, several persistent challenges remain, including: (i) selecting an appropriate sample size, (ii) determining an effective search direction, and (iii) choosing a proper step size. This paper introduces a comprehensive framework, the Stochastic Conjugate Subgradient (SCS) framework, designed to systematically address these challenges. Specifically, The SCS framework offers structured approaches to determining the sample size, the search direction, and the step size. By integrating various stochastic algorithms within the SCS framework, we have developed a novel stochastic algorithm for two-stage stochastic programming. The convergence and convergence rates of the algorithm have been rigorously established, with preliminary computational results support the theoretical analysis.

Stochastic First-Order (SFO) methods have been a cornerstone in addressing a broad spectrum of modern machine learning (ML) challenges. However, their efficacy is increasingly questioned, especially in large-scale applications where empirical evidence indicates potential performance limitations. In response, this paper proposes an innovative method specifically designed for kernel support vector machines (SVMs). This method not only achieves faster convergence per iteration but also exhibits enhanced scalability when compared to conventional SFO techniques. Diverging from traditional sample average approximation strategies that typically frame kernel SVM as an 'all-in-one' Quadratic Program (QP), our approach adopts adaptive sampling. This strategy incrementally refines approximation accuracy on an 'as-needed' basis. Crucially, this approach also inspires a decomposition-based algorithm, effectively decomposing parameter selection from error estimation, with the latter being independently determined for each data point. To exploit the quadratic nature of the kernel matrix, we introduce a stochastic conjugate subgradient method. This method preserves many benefits of first-order approaches while adeptly handling both nonlinearity and non-smooth aspects of the SVM problem. Thus, it extends beyond the capabilities of standard SFO algorithms for non-smooth convex optimization. The convergence rate of this novel method is thoroughly analyzed within this paper. Our experimental results demonstrate that the proposed algorithm not only maintains but potentially exceeds the scalability of SFO methods. Moreover, it significantly enhances both speed and accuracy of the optimization process.

Stochastic gradient-based descent (SGD), have long been central to training large language models (LLMs). However, their effectiveness is increasingly being questioned, particularly in large-scale applications where empirical evidence suggests potential performance limitations. In response, this paper proposes a stochastic conjugate subgradient method together with adaptive sampling tailored specifically for training LLMs. The method not only achieves faster convergence per iteration but also demonstrates improved scalability compared to traditional SGD techniques. It leverages sample complexity analysis to adaptively choose the sample size, employs a stochastic conjugate subgradient approach to determine search directions and utilizing an AdamW-like algorithm to adaptively adjust step sizes. This approach preserves the key advantages of first-order methods while effectively addressing the nonconvexity and non-smoothness inherent in LLMs training. Additionally, we provide a detailed analysis of the advantage of the algorithm. Experimental results show that the proposed method not only maintains, but in many cases surpasses, the scalability of traditional SGD techniques, significantly enhancing both the speed and accuracy of the optimization process.