BOT-Orch: Adaptive Agent Orchestration

• BOT-Orch is a lightweight orchestration framework that recasts sequential delegation as a bandit problem under uncertainty by integrating optimal transport for distributional alignment.
• It employs an exponential-weights scheme to balance agent reward and OT cost, enabling dynamic adaptation to shifting agent performance and non-i.i.d. task streams.
• The framework achieves sublinear O(√T) regret and demonstrates superior performance in both synthetic and semi-synthetic evaluations under non-stationarity.

BOT-Orch is a lightweight framework for adaptive orchestration of heterogeneous agents under uncertainty. It recasts sequential delegation as a bandit problem over agents, regularized by optimal-transport (OT) distances between agent output distributions and task-specific reference distributions, so that a meta-controller trades off raw reward against distributional alignment when agent reliability, cost, and response quality are uncertain or evolving (Oliver et al., 26 May 2026). In this formulation, orchestration is not treated primarily as prompt engineering or static workflow design, but as an online decision problem in which delegation policies must adapt under bandit feedback, non-i.i.d. task streams, and shifting agent behavior.

1. Conceptual framing

BOT-Orch studies orchestration in a regime where tasks arrive sequentially and the orchestrator must decide which agent to invoke without full information about unchosen alternatives. The motivating setting is adaptive coordination of specialized AI models or other heterogeneous agents whose response quality, latency, and reliability may vary over time. Prior orchestration work often optimizes for performance or cost, but BOT-Orch is explicitly motivated by the claim that uncertainty in agent reliability and output distributions is typically not modeled at the orchestration level; its central contribution is to incorporate that uncertainty through an OT-based regularizer in the online decision rule (Oliver et al., 26 May 2026).

The framework is intentionally lightweight. Rather than specifying an elaborate internal architecture for each agent, it treats each agent as a selectable action in a meta-controller’s policy. This abstraction makes the orchestration problem comparable to a multi-armed bandit, while preserving a mechanism for preferring agents whose output distributions are better aligned with task-specific references. A plausible implication is that BOT-Orch is designed less as an end-to-end agent platform than as a delegation policy layer that can sit above heterogeneous backends.

2. Formal problem setting

Let $\mathcal{A}=\{a_1,\ldots,a_M\}$ be a finite set of heterogeneous agents, and let tasks arrive over rounds $t=1,\ldots,T$. At round $t$ the orchestrator observes a context $x_t\in\mathcal{X}$ drawn from a possibly non-i.i.d., history-dependent process $\mathcal{P}(\cdot\mid \mathcal{H}_t)$, where

$$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$

collects past tasks, selected agents, realized rewards, and OT costs. If agent $a_i$ is chosen, it yields a stochastic reward $R_t^i\in[0,R_{\max}]$ and incurs an alignment cost $W_t^i$. The conditional means are written

$$r^i(x_t)=E[R_t^i\mid x_t], \qquad w^i(x_t)=E[W_t^i\mid x_t].$$

The online objective is to learn a policy $t=1,\ldots,T$0 maximizing cumulative net utility

$t=1,\ldots,T$1

where $t=1,\ldots,T$2 controls the reward–alignment trade-off. Regret is defined against an oracle that, at each round, selects

$t=1,\ldots,T$3

The resulting regret,

$t=1,\ldots,T$4

measures the penalty of online orchestration relative to round-wise optimal delegation (Oliver et al., 26 May 2026).

BOT-Orch uses standard bandit feedback. Each agent is treated as a bandit arm, and when arm $t=1,\ldots,T$5 is pulled at time $t=1,\ldots,T$6 the learner observes $t=1,\ldots,T$7 and receives instantaneous utility

$t=1,\ldots,T$8

Only the chosen arm’s utility is observed. This is consequential: the orchestrator must adapt without counterfactual access to the rewards and alignment costs of unselected agents.

3. Optimal-transport regularization

The distinctive feature of BOT-Orch is its alignment term. For each task, an agent’s uncertain output distribution $t=1,\ldots,T$9 is compared to a task-specific reference distribution $t$0 using the $t$1-Wasserstein distance with ground cost $t$2:

$t$3

Under assumption (A1), the ground cost is $t$4-Lipschitz and bounded, so the OT term is well-behaved. The paper models the realized alignment cost as

$t$5

and then penalizes agents proportionally to this cost (Oliver et al., 26 May 2026).

This construction makes OT a first-class orchestration signal rather than a post hoc evaluation metric. The single-round surrogate objective becomes $t$6, and for a mixed policy $t$7 the orchestrator maximizes $t$8. The regularizer therefore does not merely reward high average performance; it prefers agents whose output distributions are closer to task-specific references. In the paper’s terms, BOT-Orch provably induces a preference ordering among agents with identical mean rewards but differing distributional alignment.

4. Algorithmic mechanism

BOT-Orch instantiates an exponential-weights, or softmax, scheme with OT-adjusted rewards. The algorithm begins from uniform weights $t$9 for all agents and uses an inverse temperature $x_t\in\mathcal{X}$0. At round $x_t\in\mathcal{X}$1, it forms the policy

$x_t\in\mathcal{X}$2

samples an agent $x_t\in\mathcal{X}$3, observes $x_t\in\mathcal{X}$4 and $x_t\in\mathcal{X}$5, and updates only the chosen arm:

$x_t\in\mathcal{X}$6

while leaving $x_t\in\mathcal{X}$7 for $x_t\in\mathcal{X}$8 (Oliver et al., 26 May 2026).

In practical implementations, the paper notes that one maintains running estimates $x_t\in\mathcal{X}$9 of $\mathcal{P}(\cdot\mid \mathcal{H}_t)$0, for example via exponential smoothing or a Robbins–Monro update, and computes current OT costs by solving small optimal-transport problems using Sinkhorn or closed form in low-dimensional output spaces. The stated complexity per round is $\mathcal{P}(\cdot\mid \mathcal{H}_t)$1 for the softmax update plus the cost of $\mathcal{P}(\cdot\mid \mathcal{H}_t)$2 OT computations, such as $\mathcal{P}(\cdot\mid \mathcal{H}_t)$3 per distribution match, though often smaller in outcome space. This computational structure is modest compared with systems that require multiple concurrent agents and multi-stage merge procedures.

5. Theoretical properties

Under assumptions (A1)–(A5), including bounded rewards, $\mathcal{P}(\cdot\mid \mathcal{H}_t)$4-Lipschitz ground cost, and sub-Gaussian frailty noise, BOT-Orch achieves sublinear OT-regularized pseudo-regret. The main guarantee states that with $\mathcal{P}(\cdot\mid \mathcal{H}_t)$5,

$\mathcal{P}(\cdot\mid \mathcal{H}_t)$6

The proof sketch follows the standard multiplicative-weights analysis for bounded utilities $\mathcal{P}(\cdot\mid \mathcal{H}_t)$7, yielding the usual trade-off between exploration and cumulative regret; martingale concentration is used to handle data-dependent sampling (Oliver et al., 26 May 2026).

A second theoretical property is the preference-ordering effect. If two agents satisfy $\mathcal{P}(\cdot\mid \mathcal{H}_t)$8 but have different alignment costs, then

$\mathcal{P}(\cdot\mid \mathcal{H}_t)$9

because $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$0. This means that equal-mean agents are no longer indistinguishable: the one whose output distribution is closer, in Wasserstein distance, to the task reference is strictly preferred. The paper identifies this as structural OT-optimality, supported by a proposition stating that if $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$1 but $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$2, then $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$3.

6. Empirical evaluation

The empirical study uses synthetic adversarial allocation in both i.i.d. and non-i.i.d. regimes across five environments: IID–G, with fixed Gaussian rewards and heterogeneous variance, skewness, and bimodality; IID–M, with half-moon task features and distributionally heterogeneous reward laws; NonIID–PS, with piecewise-stationary variances; NonIID–SD, with smoothly drifting sinusoidal reward means; and NonIID–BB, with Brownian-bridge evolution of latent means. Baselines are No-OT with $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$4, Random uniform, and UCB1 classic MAB. Evaluation uses cumulative net utility $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$5, cumulative alignment cost $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$6, and oracle regret $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$7 (Oliver et al., 26 May 2026).

For $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$8, BOT-Orch attains the highest net utility and lowest regret in all settings, with particularly large gains under non-stationarity. The paper reports that an ablation over $$\mathcal{H}_t=\sigma(x_1,A_1,R_1,W_1;\ldots;x_{t-1},A_{t-1},R_{t-1},W_{t-1})$$9 shows performance peaking around $a_i$0. This result is consistent with the framework’s intended role: the OT regularizer is not ancillary, since performance degrades when it is removed.

The paper also includes a semi-synthetic human–AI triage study on Breast Cancer Wisconsin data. Two agents, an AI classifier and a human expert, are simulated with complementary accuracies under distribution shift. In this setting, OT costs reduce to $a_i$1–$a_i$2 label-space Wasserstein distances,

$a_i$3

With $a_i$4, BOT-Orch achieves the highest cumulative net utility, approximately $a_i$5 versus $a_i$6 for No-OT, the lowest oracle regret, approximately $a_i$7 versus $a_i$8, and high team accuracy, about $a_i$9 versus $R_t^i\in[0,R_{\max}]$0. It also dynamically escalates more to the human under shift, which the paper presents as evidence of effective adaptation (Oliver et al., 26 May 2026).

7. Position within orchestration research

BOT-Orch belongs to a broader family of orchestration systems, but it occupies a distinct design point. AOrchestra, for example, models any agent as the tuple $R_t^i\in[0,R_{\max}]$1 of Instruction, Context, Tools, and Model, and its central orchestrator concretizes that tuple at each step to curate context, select tools and models, and delegate execution through on-the-fly automatic agent creation. It reports gains on GAIA, SWE-Bench, and Terminal-Bench and emphasizes controllable performance–cost trade-offs (Ruan et al., 3 Feb 2026). ORCH, by contrast, is a deterministic multi-agent orchestrator for discrete-choice reasoning built around a “many analyses, one decision” paradigm with fixed decomposition and merge rules, plus an optional EMA-guided router (Zhou et al., 2 Feb 2026). ORCHID addresses high-risk property classification through an orchestrated retrieval-augmented workflow with human oversight, append-only audit bundles, and Model Context Protocol tooling for on-premise operation (Mahbub et al., 7 Nov 2025).

These systems focus on different aspects of orchestration: dynamic sub-agent construction, deterministic merge-based reasoning, and auditable human-in-the-loop compliance workflows. BOT-Orch is narrower in architectural scope but more explicit in its online learning formulation. This suggests that it is best understood as a principled uncertainty-aware delegation policy rather than as a complete orchestration stack. Its contribution is the formalization of orchestration under uncertainty with OT-regularized bandit feedback, together with an $R_t^i\in[0,R_{\max}]$2 regret guarantee and evidence of robustness in non-i.i.d. settings (Oliver et al., 26 May 2026).

BOT-Orch is also unrelated to Orch OR, the consciousness proposal centered on gravity-induced objective reduction and orchestrated collapses in microtubules (McQueen, 2023). The shared string “Orch” reflects different uses of “orchestration”: in BOT-Orch it denotes meta-control over heterogeneous agents, whereas in Orch OR it refers to the “orchestrated” component of a quantum-consciousness hypothesis.