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arxiv: 2605.07572 · v1 · submitted 2026-05-08 · 💻 cs.AI · stat.ML

Recognition: no theorem link

Open-Ended Task Discovery via Bayesian Optimization

Masaki Adachi , Yuta Suzuki , Juliusz Ziomek

Authors on Pith no claims yet

Pith reviewed 2026-05-11 02:42 UTC · model grok-4.3

classification 💻 cs.AI stat.ML
keywords Bayesian optimizationtask discoveryopen-ended optimizationregret analysisscientific workflowsGenerate-Select-RefineLLM optimizers
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The pith

A Generate-Select-Refine loop lets Bayesian optimization discover new tasks from a seed while concentrating evaluations on the best one with only logarithmic extra regret.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents GSR, a framework that begins with one user-supplied seed task and repeatedly generates new candidate tasks in a coarse-to-fine sequence. A separate task-acquisition function then decides how to allocate optimization effort across the growing set of tasks. The central guarantee is that, asymptotically, the method devotes nearly all evaluations to the single best task found, adding only a logarithmic regret penalty compared with running standard Bayesian optimization on that task alone. This setup is demonstrated on product development, chemical scaling, algorithm analysis, and patent work, where it beats fixed-task and existing LLM-based baselines. The approach matters because many scientific problems involve uncertainty not only about parameter values but about which objective should be optimized in the first place.

Core claim

GSR alternates task generation with scheduled optimization across the generated tasks. Starting from a seed task, it produces new tasks in a coarse-to-fine manner; a task-acquisition function then chooses which task to optimize next. Asymptotically the procedure concentrates evaluations on the single best task discovered, incurring only logarithmic regret overhead relative to ordinary single-task Bayesian optimization.

What carries the argument

The Generate-Select-Refine (GSR) loop, which generates tasks from a seed and uses a task-acquisition function to schedule Bayesian optimization across them.

If this is right

  • In new-product or chemical-synthesis settings the method can locate improved objectives without a separate manual task-design phase.
  • The regret analysis shows that discovering tasks does not force linear extra cost; only log(T) additional evaluations are needed in the limit.
  • Existing LLM-based optimizers are outperformed on the four application domains tested.
  • The framework supplies a concrete mechanism for open-ended task evolution inside the Bayesian optimization loop.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same scheduling idea could be tested on non-Bayesian optimizers to see whether the logarithmic overhead persists.
  • In machine-learning practice, GSR suggests a way to let models propose and compare their own evaluation metrics rather than fixing them in advance.
  • If task generation is replaced by an external oracle that occasionally supplies better tasks, the regret bound would still apply and could guide resource allocation in automated science pipelines.

Load-bearing premise

The generation procedure, begun from a user seed, must keep producing useful new tasks in a coarse-to-fine order that the acquisition function can reliably rank and allocate effort toward.

What would settle it

Run GSR on a domain where every generated task is strictly worse than the seed; if the total number of evaluations needed to identify the seed as best still exceeds the logarithmic overhead bound, the concentration claim is false.

Figures

Figures reproduced from arXiv: 2605.07572 by Juliusz Ziomek, Masaki Adachi, Yuta Suzuki.

Figure 1
Figure 1. Figure 1: Conceptual overview: Starting from a seed task i0, the new tasks are iter￾atively generated toward the ϵ-optimal task i ⋆ and identifies its optimum x ⋆ . (a) Exper￾imental progress: task generation and elim￾ination over time. (b) Two-loop structure: feedback from within-task BO informs task refinement via a coarse-to-fine scheduler. Bayesian optimization (BO; [28]) is a sample-efficient black-box optimize… view at source ↗
Figure 3
Figure 3. Figure 3: LLM components in GSR: (Left) Coarse-to-fine task generation: we mutate a parent task with target mutation ratio ρm, producing refined tasks. (Right) Committee-based evaluation: committee returns binary votes if the current task–incumbent pair (i, y (i) s ) is preferred over an anchor (at, y (at) s ). By averaging them, we estimate a confidence interval for the utility u (i) (y (i) s ). Task Selection. Cor… view at source ↗
Figure 2
Figure 2. Figure 2: Alg. 1: (a) Select chooses the next task it and anchor task at. (b) Refine ad￾vances the resolution levels ϵ U m and generates J mutations when anchor width wt ≤ cgϵ U m. Task Refinement. We generate new tasks by mutat￾ing and iteratively refining a seed task. A key step is selecting an anchor task to mutate. The anchor must be both promising and sufficiently resolved. We therefore choose at as the most pr… view at source ↗
Figure 4
Figure 4. Figure 4: Real-world experiments. Top row: planning tasks—(a) new product development and (b) [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: GSR’s task evolution tree shows coarse-to-fine refine￾ment across levels m toward the best task (20). Colors indicate fi￾nal utility, and evaluation counts vary across tasks; task (1) ini￾tially lags behind its children (4–6), improves with more BO evaluations, and is ultimately surpassed by task (20). We first apply GSR to planning, where one must decide both what to optimize and how to evaluate it, start… view at source ↗
Figure 6
Figure 6. Figure 6: Resolution controllability. (a) Mutation ratio ρm correlates with task distance. (b) finer task generation prob￾ability δ+ is non-zero across all reso￾lution levels m. (c) Finer mutations yield higher δ+. (d) Coarser mutations achieve larger improvement. Patent Repurposing. In industrial R&D, materials devel￾oped for a target application are often abandoned despite substantial sunk costs; repurposing aims … view at source ↗
Figure 7
Figure 7. Figure 7: Unknown search space. Resolution controllability. We analyze the LLM exper￾iments using the white wine task. GSR uses mutation to control task resolution. We generate J = 40 child tasks for 4 anchor tasks across mutation ratios ρm, reso￾lution levels m, and random seeds (Fig.6). (a) Task dis￾tance—Euclidean distance over numerical task parame￾ters—correlates with ρm, confirming that JSON mutation controls … view at source ↗
Figure 8
Figure 8. Figure 8: Offline settings: (a) Fixed task selection and (b) objective selection. Offline experiments. Finally, we consider an offline set￾ting with no generator: all tasks are fixed a priori, reducing the problem to task selection. Algorithm 1 thus simplifies to pure task-UCB (omitting Lines 8–10). We evaluate six BoTorch benchmark functions, defining task utilities via a Gaussian CDF, u (i) (yt ) := Φ y (i) t − µ… view at source ↗
Figure 9
Figure 9. Figure 9: Log-odds chain rule: adding logits and mapping back with sigmoid offers cardinal utility [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Alg. 2: We hold multiple candidate Lipschitz bounds [PITH_FULL_IMAGE:figures/full_fig_p036_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Ablation study. Replacing the mutation scheduler [PITH_FULL_IMAGE:figures/full_fig_p058_11.png] view at source ↗
read the original abstract

When applying Bayesian optimization (BO) to scientific workflow, a major yet often overlooked source of uncertainty is the task itself -- namely, what to optimize and how to evaluate it -- which can evolve as evidence accumulates. We introduce Generate-Select-Refine (GSR), a open-ended BO framework that alternates between task generation and task optimization. Starting from a user-provided seed task, GSR generates new tasks in a coarse-to-fine manner while a task-acquisition function schedules optimization. Asymptotically, it concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO. We apply GSR to new product development, chemical synthesis scaling, algorithm analysis, and patent repurposing, where it outperforms existing LLM-based optimizers.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The paper introduces the Generate-Select-Refine (GSR) framework for open-ended Bayesian optimization. Starting from a user-provided seed task, GSR alternates task generation (coarse-to-fine, LLM-driven) with optimization scheduled by a task-acquisition function. The central claim is that asymptotically GSR concentrates evaluations on the best task while incurring only logarithmic regret overhead relative to single-task BO. Empirically, GSR is applied to new product development, chemical synthesis scaling, algorithm analysis, and patent repurposing, where it outperforms existing LLM-based optimizers.

Significance. If the asymptotic regret bound can be rigorously closed and the empirical results are shown to be robust, this would represent a meaningful extension of BO to settings with evolving task definitions. The multi-domain applications illustrate potential utility in LLM-augmented scientific workflows, and the framework's structured alternation between generation and selection is a constructive contribution even if the regret analysis requires strengthening.

major comments (2)
  1. [Abstract] Abstract: The claim that GSR 'concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO' is load-bearing for the contribution but lacks a supporting formal model. No explicit task space (finite or hierarchically structured) is defined, nor is there a proof that the generation step produces non-decreasing task quality; without this, the regret analysis cannot be closed, as the generator could indefinitely introduce incomparable or inferior tasks.
  2. [Empirical evaluation] Empirical evaluation section: The reported outperformance over LLM-based optimizers is presented without accompanying details on the number of independent runs, variance estimates, statistical tests, or direct comparison against single-task BO (the theoretical baseline). This gap prevents assessment of whether the results support the asymptotic claim or are robust across the four listed domains.
minor comments (1)
  1. The task-acquisition function is referenced but its precise mathematical form is not stated in the abstract; adding a short equation or pseudocode reference would improve clarity for readers unfamiliar with the scheduling mechanism.

Simulated Author's Rebuttal

2 responses · 0 unresolved

Thank you for the thoughtful review. We will revise the manuscript to strengthen the formal foundations of the regret analysis and enhance the empirical evaluation with additional statistical details and comparisons.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The claim that GSR 'concentrates evaluations on the best task, incurring only logarithmic regret overhead relative to single-task BO' is load-bearing for the contribution but lacks a supporting formal model. No explicit task space (finite or hierarchically structured) is defined, nor is there a proof that the generation step produces non-decreasing task quality; without this, the regret analysis cannot be closed, as the generator could indefinitely introduce incomparable or inferior tasks.

    Authors: We agree that a more rigorous formal model would strengthen the paper. In the revised version, we will explicitly define the task space as a tree-structured hierarchy where each generation step refines parent tasks, and provide a lemma showing that under the assumption of the LLM generator improving task quality in expectation (based on the coarse-to-fine process), the task-acquisition function ensures logarithmic regret overhead. This addresses the potential for introducing inferior tasks by incorporating a quality threshold in the generation step. revision: yes

  2. Referee: [Empirical evaluation] Empirical evaluation section: The reported outperformance over LLM-based optimizers is presented without accompanying details on the number of independent runs, variance estimates, statistical tests, or direct comparison against single-task BO (the theoretical baseline). This gap prevents assessment of whether the results support the asymptotic claim or are robust across the four listed domains.

    Authors: We will expand the empirical section to include: (i) results averaged over 20 independent runs per domain with standard error bars, (ii) Wilcoxon signed-rank tests for significance, and (iii) a direct comparison to single-task BO on the seed task, demonstrating that the additional overhead from task discovery is indeed logarithmic in the number of evaluations. These additions will confirm robustness across the domains of new product development, chemical synthesis, algorithm analysis, and patent repurposing. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper defines the Generate-Select-Refine (GSR) framework explicitly from a user-provided seed task and positions its asymptotic concentration claim as a theoretical comparison to single-task Bayesian optimization, which serves as an external benchmark rather than an internal input. No self-definitional reductions, fitted parameters renamed as predictions, or load-bearing self-citations are present in the abstract or described process. The task-acquisition scheduling and coarse-to-fine generation are introduced as independent components, and the regret overhead statement does not reduce to a tautology of the framework's own definitions. The derivation chain remains self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim depends on the effectiveness of the task generation and selection process, which is introduced without detailed justification in the abstract.

axioms (1)
  • domain assumption Task generation from a seed task can produce meaningful variations in a coarse-to-fine manner
    The framework relies on this to create new tasks for optimization.
invented entities (1)
  • Generate-Select-Refine (GSR) framework no independent evidence
    purpose: To enable open-ended task discovery and optimization in Bayesian optimization
    New framework introduced to alternate between task generation and optimization.

pith-pipeline@v0.9.0 · 5422 in / 1295 out tokens · 47852 ms · 2026-05-11T02:42:33.405363+00:00 · methodology

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Cited by 1 Pith paper

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