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Learning-Augmented Algorithms: Guarantees, Construction Mechanisms, and System-Level Implications

Hailiang Zhao, Peng Chen, Xueyan Tang, Jianwei Yin, Shuiguang Deng

arXiv:2609.04787v1cs.LGcs.DS

TL;DR

The survey addresses how algorithms can use fallible predictions while retaining formal guarantees, and how those guarantees should be interpreted across components and deployments. It synthesizes prediction interfaces, error measures, construction mechanisms, theorem-level evidence, and system considerations. The resulting framework separates proved frontiers, achieved upper bounds, and empirical systems evidence while identifying boundaries for composition and semantic prediction.

  • Problem

    The survey examines how to use fallible predictions with formal guarantees while accounting for prediction cost, feedback, composition, and the distinction between achieved and matched theorem-level bounds.

  • Method

    The paper conducts a structured narrative survey organized by five non-exclusive construction mechanisms and an orthogonal axis for matched asymptotic dependence.

  • Results

    The synthesis distinguishes theorem-specific consistency, robustness, and error-dependent guarantees from empirical systems evidence and identifies limited conditions for end-to-end reasoning.

  • Takeaways & Limitations

    Formal component guarantees should not be treated as automatically composing across systems, especially when components face induced instances, feedback, and different benchmarks.

  • Takeaways & Limitations

    The review is a structured narrative survey based on targeted search rather than an exhaustive systematic review, and its taxonomy is qualitative rather than a prevalence estimate.

Abstract

from arXiv · show

Learning-augmented algorithms use fallible predictions while retaining formal performance guarantees. This survey synthesizes prediction interfaces, error measures, consistency--robustness trade-offs, and five representative construction mechanisms across online optimization, caching, learned data structures, graph problems, and mechanism design. An orthogonal theorem-level axis distinguishes achieved upper bounds from matched asymptotic dependence. Formal guarantees are separated from empirical systems evidence, with explicit treatment of prediction cost, feedback, and composition. The resulting synthesis states sufficient conditions for limited end-to-end reasoning and delineates open problems in cost-aware prediction, endogenous error, semantic predictors, and benchmarking.

1 Introduction

The survey frames learning-augmented algorithms as a formal interface for using fallible predictions while distinguishing consistency, robustness, and intermediate-error behavior. It extends this view toward deployment through a system-level perspective that makes prediction, decision, actuation, monitoring, and omitted assumptions explicit.

  • Motivation: Cloud scenarios show how stale predictors, unbounded learned policies, and hidden prediction costs can undermine deployment reasoning.The examples cover autoscaling, caching, and query planning under changing workloads, out-of-distribution requests, and schema migration.
  • Formal interface: Learning-augmented algorithms distinguish behavior under perfect predictions, arbitrary predictions, and intermediate prediction error.These correspond to consistency, robustness, and smoothness-style guarantees, respectively.
  • Deployment gap: Prediction computation, feedback, retraining, and cross-component effects usually remain outside component objectives.Robustness is commonly proved for adversarial inputs, which is distinct from assuming stationarity.
  • System-level perspective: Learning-augmented systems provide an organizing perspective that exposes prediction, decision, actuation, monitoring, and omitted costs without automatically composing component guarantees.The survey states that limited end-to-end reasoning requires additional sufficient conditions and that semantic predictors need new models and proofs.
  • Survey scope: The survey classifies where predictions enter constructions and examines assumptions needed when components share compute, state, and failure domains.This classification is presented as a targeted synthesis rather than an exhaustive partition of the literature.

2 Scope and Method

The survey uses a structured narrative review to organize technical devices, theorem-level trade-offs, system assumptions, and the status of foundation-model predictions. Its taxonomy is qualitative and non-exhaustive, with explicit boundaries around corpus coverage, empirical evidence, and matched-bound claims.

  • Research questions: The survey asks which mechanisms yield provable guarantees, which dependencies have matched lower bounds, which system assumptions need modeling, and what remains unsupported for foundation-model predictions.These four questions organize the scope and method.
  • Corpus construction: The corpus combines prior surveys, the ALPS index, citation snowballing, and targeted searches through 3 September 2026.Queries covered application, mechanism, prediction-budget, uncertainty, and foundation-model terms.
  • Review design: The review is a structured narrative survey rather than a registered systematic review, with no deduplicated screening log or PRISMA counts.Its records support checking representative claims but do not constitute an exhaustive claim-level audit.
  • Inclusion and exclusion: The core corpus requires stated consistency, robustness, or explicit error-dependent guarantees, while empirical or average-case gains remain adjacent evidence.Offline learning of a fixed configuration and advice complexity without an error-sensitive guarantee are outside the core corpus.
  • Taxonomy: Axis A classifies five non-exclusive prediction-entry mechanisms, while Axis B records whether theorem dependence is achieved or matched in the same model.E1 requires agreement on every model-defining dimension; E0 records no matched lower bound in the survey’s formal model.
  • Theorem-level audit: The E0/E1 coding compares prediction object, adversary, benchmark, objective, error, and bound assumptions at theorem level.No independent second coder or inter-rater statistic is reported, so the tables are navigation aids rather than prevalence estimates.
  • Relation to prior work: The survey’s organization complements prior classifications by prediction type, warm-start versus online use, and advice information without treating those axes as interchangeable.A full sequence of next-request predictions may contain more information than an advice bound with the same per-symbol alphabet.
  • Validity boundaries: The taxonomy is a working set based on targeted search, not evidence that unassigned combinations are empty.Systems analogies to robustifiers, fallbacks, or restricted action spaces remain architectural unless a reduction is stated.

3 Background and Formal Framework

The survey fixes notation for prediction-aware guarantees, separates consistency, robustness, and smoothness, and emphasizes that prediction objects, error measures, and theorem tightness must be interpreted under aligned assumptions. A ski-rental example illustrates the resulting trade-offs and the limits of adaptive trust.

  • 3.1 Notation: Notation distinguishes the instance I, observable information z(I), prediction ŷ=P(z(I)), target y*(I), problem-specific loss, algorithmic cost, and offline optimum OPT(I).The algorithm receives no unrevealed part of I, while expectations range over the probability space declared by the theorem.
  • 3.2 Evaluation Criteria: The trust parameter λ is chosen before the unrevealed instance is seen, with smaller λ denoting greater trust in this survey.The parameter cannot depend on realized error when that error is unavailable online.
  • 3.2 Evaluation Criteria: Consistency bounds cost under exact predictions, robustness gives an error-independent bound for arbitrary predictions, and smoothness provides a non-decreasing error-dependent envelope.Smoothness recovers consistency at zero error and implies robustness only when its envelope is uniformly bounded.
  • 3.2 Evaluation Criteria: Consistency–robustness pairs are tight only when a matching lower bound rules out every dominating pair in the same formal model.Smoothness is not itself robustness, and a Pareto-optimal endpoint pair need not control performance at small nonzero error.
  • 3.3 Prediction Objects and Representations: Prediction objects include point, distributional, ordinal, and structural outputs, while uncertainty annotations and representations qualify task objects without determining a single paradigm.The taxonomy treats task objects, uncertainty information, and interface representations as distinct levels.
  • 3.4 How Error Is Measured: Error curves are comparable only when loss definitions, normalization, aggregation, and benchmarks align; late-revealed targets support ex post analysis but cannot directly control an online deployment.Operational deployment instead needs timely proxies, constraints, or reversible fallback rules.
  • 3.5 A Running Example: Ski Rental: For ski rental, the deterministic rule yields c(λ)=1+λ, r(λ)=1+1/λ, and normalized-error envelope f_λ(η)=1+λ+η/(1−λ).At B=100 and λ=1/2, the guarantees are c≤1.5 and r≤3; as λ→0, consistency approaches 1 while robustness diverges.

4 Design Paradigms for Learning-Augmented Algorithms

The survey organizes learning-augmented constructions into five non-exclusive mechanisms and separately records whether theorem bounds have matched asymptotic lower bounds. This separation preserves differences in prediction objects, feedback, objectives, and evidence status.

  • Taxonomy: Axis A uses five non-exclusive labels for recurring construction mechanisms, while Axis B independently records theorem-level tightness.E1 requires matching asymptotic dependence under the same model; otherwise the survey records E0.
  • P1: Trust-Based Combination: Trust-based combination mixes a prediction-following algorithm with a robust algorithm through a fixed trust parameter.Randomized mixtures yield c(λ) ≤ (1 − λ)c_c + λα_r, but an unbounded prediction-following branch remains non-robust for λ < 1.
  • P1: Trust-Based Combination: Parameterized interpolation continuously tunes one decision rule to trace a consistency–robustness Pareto frontier.For ski rental, the deterministic curve is (1 + λ, 1 + 1/λ) and is asymptotically Pareto-optimal as B grows.
  • P3: Prediction-Sensitive Relaxation and Rounding: Prediction-sensitive relaxation and rounding first constructs a prediction-guided fractional solution, then applies an online rounding theorem to obtain an integral guarantee.If the fractional stage is g(η)-competitive and rounding incurs factor ρ, the combined guarantee is ρg(η).
  • P4: Prediction-Access, Portfolio, and Switching Reductions: Portfolio and switching reductions require a problem-specific link from predictor choice to actual cost, compatible state or migration rules, and an appropriate comparator.Adversarial regret against non-robust experts alone does not establish robustness.
  • P5: Distributional Prediction: Distributional prediction mechanisms analyze advice about an access distribution rather than a point, using problem-specific objectives and stability assumptions.The survey rejects a universal coherent-risk or Lipschitz principle because risk measures and distributional guarantees require distinct assumptions.
  • Scope and evidence: The survey’s taxonomy is illustrative rather than exhaustive, and grouped domain records do not receive a single evidence label across incomparable guarantees.Unlisted mechanism–domain combinations remain search and modeling questions rather than asserted research gaps.

5 Problem Domains

The survey compares learning-augmented methods across stopping, stateful, convex, allocation, and scheduling domains while preserving each problem’s objective and prediction model. Tight results are concentrated in selected well-specified models, whereas many higher-dimensional results remain upper bounds under distinct assumptions.

  • Classical formulations: Online optimization defines sequential decisions under revealed history, with competitive ratio comparing algorithmic cost against an offline optimum obeying the same constraints.Ski rental has deterministic optimum ratio 2 and randomized optimum ratio e/(e−1) ≈ 1.58.
  • Stopping problems: Deterministic ski rental has trade-off (1 + λ, 1 + 1/λ), with an asymptotically matching impossibility frontier as B grows.Approaching exact 1-consistency sends the deterministic robustness bound to infinity; randomized frontiers differ.
  • Stopping problems: Stopping variants extend the framework to expiration and residual-value effects in Bahncard and multiple power-saving states in dynamic power management.These models change the prediction target and cost structure relative to ski rental.
  • Stateful decision-making: Metrical task systems trade movement cost against service cost while maintaining states in a metric space, so adversary and randomization models must be specified.Classical deterministic guarantees scale linearly with the number of metric points.
  • Stateful decision-making: Prediction-access and portfolio methods for metric problems obtain problem-specific guarantees under constrained switching, bandit access, and delayed feedback.One cited lower bound leaves logarithmic factors, so the survey records E0 under its strict same-asymptotics rule.
  • Convex optimization: Online convex optimization uses predicted gradients or losses to replace horizon-only regret bounds with bounds depending on cumulative hint error under stated geometry and regularity assumptions.These are point-prediction regret guarantees, not distributional optimization results.
  • Resource allocation and scheduling: Resource-allocation and scheduling results use problem-specific prediction objects, error measures, and objectives, including learned weights for fractional schedules followed by online rounding.Comparisons require matching the prediction object, objective, feedback, and error metric.
  • Cross-domain assessment: The surveyed domains differ in objective and evidence maturity: tight bounds cluster in selected models, while graph, data-structure, and mechanism-design results often optimize incomparable quantities.Upper bounds should not be treated as complete characterizations without matching lower bounds.

5.2 Caching and Paging

Learning-augmented caching uses predictions to guide eviction while combining consistency, robustness, and error-sensitive guarantees with classical paging methods. The section also highlights costs that standard competitive analyses omit, including switching, query access, and predictor inference.

  • Classical foundations: Classical paging benchmarks provide the baseline for evaluating prediction-guided eviction under deterministic and randomized models.Deterministic paging has competitive ratio k, while randomized paging is benchmarked against H_k.
  • Prediction interfaces: Next Request Time predictions approximate Belady’s oracle, whereas binary or action predictions provide coarser eviction guidance.NRT predicts a page’s next request timestamp; binary predictions indicate reuse within a window or recommend eviction directly.
  • Consistency and robustness: Switching between prediction-following and classical paging algorithms must charge cache-state coupling costs rather than choosing a prediction-dependent parameter after observing error.Query complexity, running time, and competitive ratio are distinct resources.
  • Consistency and robustness: Guard&A preserves 1-consistency and achieves (2H_k−1 + 2)-robustness for specified RB-following caching algorithms.The guarantee preserves the base algorithm’s asymptotic running time but relies on paging-specific phase and protection rules and excludes predictor inference overhead.
  • Prediction interfaces: One-bit succinct predictions support consistency, robustness, and smoothness guarantees together with lower bounds in the same advice model.The model does not assume Markov-chain or aggregate Markov predictors.
  • Open gaps: Caching results leave open error concentration, time-varying colocated capacity, and objective models that include inference latency or energy.Query-budget studies count predictor use, but do not by themselves convert inference cost into the caching objective.

5.3 Learned Data Structures

Learned data structures use models to narrow searches, adapt layouts, or filter queries, but their guarantees depend on certified error, workload regularity, update behavior, and complete resource accounting. Related graph results similarly show that prediction can improve running time or approximation only under problem-specific prediction objects and guarantees.

  • Learned indexes: Learned indexes narrow search intervals using fitted models, so gains require accounting for model space, inference time, and correction structures.The improvement is conditional on data regularity and does not replace ordered-search semantics.
  • Learned indexes: A certified position-error bound ε_θ yields local binary-search cost O(log(ε_θ + 1)), alongside model-space and inference costs.The resulting trade-off depends on workload and architecture rather than defining a universal Pareto frontier.
  • Worst-case guarantees: Worst-case learned-index behavior requires a certified error bound plus a larger-range or full-index fallback, typically recovering O(log n).A fitted-structure bound ε_θ ≤ ε̄ is not robustness to arbitrary prediction error.
  • Worst-case guarantees: The PGM-index uses Θ(m) space for the minimum m of ε-approximate segments, with worst-case upper bound m ≤ n/(2ε).This is an upper bound, not a claim that every dataset requires Θ(n/ε) space; the construction also has a dynamic variant.
  • Adaptive layouts: ALEX combines learned linear models, gapped-array nodes, cost models, and adaptive splitting or expansion to support updates empirically.It does not establish a consistency–robustness theorem under distribution shift.
  • Filters: Learned Bloom filters combine a classifier with a backup Bloom filter, so false-positive performance depends on classifier behavior, query distribution, and backup memory.Perfect classifier precision alone does not force total false positives to zero, and classical dominance is not automatic for every allocation.
  • Open gaps: Open learned-index questions include adversarial updates, rebuild policy, retraining cost, memory movement, and state migration for model portfolios.Benchmark performance varies across insertion patterns and datasets.
  • Graph problems: Incremental shortest-path structures can use predicted edge-insertion sequences to warm-start state while retaining (1+ε)-approximate distances and error-dependent running time.The result recovers a worst-case bound up to logarithmic factors and concerns dynamic running time rather than a consistency–robustness ratio.

5.5 Mechanism Design and Algorithmic Game Theory

Learning-augmented mechanism design incorporates predictions while preserving a declared incentive notion, but guarantees remain tied to the strategic model, objective, and prediction interface. Revenue, welfare, and online-selection results therefore cannot be transferred across mechanisms or arrival models without preserving their assumptions.

  • Incentive constraints: Mechanism-design guarantees must distinguish DSIC, which requires truthfulness for every report profile, from BIC, which is expectation-based.Learning-augmented mechanisms use predictions of values, processing times, locations, or other side information while preserving a specified incentive notion.
  • Scheduling: Predicted processing times can support strategyproof scheduling mechanisms with consistency and robustness guarantees.The cited setting concerns unrelated-machine scheduling rather than auction reserves.
  • Auctions and pricing: Revenue-sensitive mechanisms must specify how prediction error changes revenue while preserving the declared incentive property.This is especially relevant when revenue depends on distributional assumptions and reserve prices.
  • Auctions and pricing: Mechanism combination preserves DSIC only when branch selection and payments prevent agents from manipulating which mechanism is used.Ordinary switching is insufficient; prior-free meta-mechanisms can instead use side information and weakest-competitor constructions.
  • Online selection: Secretary, prophet-inequality, and online bipartite-matching models have different classical benchmarks and should not be collapsed into one 1/e barrier.Their standard benchmarks are 1/e success probability, 1/2 factor, and 1 − 1/e, respectively.
  • Online selection: Advice-based guarantees do not transfer across arrival models, and thresholding, randomized rounding, and portfolio selection are distinct constructions.Fairness variants and predicted-order models require their own assumptions.
  • Contracts and information design: Prediction-dependent objectives in contracts and Bayesian persuasion must be analyzed with the relevant incentive and best-response constraints.A worst-case expected-utility lens around a predicted distribution is distinct from robust Bayesian persuasion.
  • Open gaps: Strategic agents may manipulate predictor inputs, making prediction error an equilibrium object rather than a fixed exogenous parameter.Instance-optimal benchmarks are also delicate when the comparison class must satisfy incentive constraints.

5.6 Cross-Cutting Methodological Developments

Cross-cutting work treats prediction generation, query access, uncertainty, and portfolios as part of the algorithmic design rather than as invisible inputs. The survey finds that these directions remain problem-specific, with unresolved links between prediction quality, downstream cost, and end-to-end guarantees.

  • System boundaries: Most theory conditions on advice and leaves predictor training, query frequency, and changing observation–outcome relationships outside the theorem.These omissions constrain direct system-level interpretation.
  • System boundaries: The survey treats prediction generation, query budgets, and uncertainty representation as design variables that can affect guarantees.The consuming algorithm alone does not determine the full guarantee.
  • Methodological threads: The survey distinguishes four established methodological threads from two directions whose guarantees remain conditional or incomplete.The threads concern learning the prediction, budgeting queries, using portfolios, and quantifying uncertainty.
  • Learning the prediction: Decision-focused training, algorithm-aware learning, and explicit-predictor algorithms attempt to align learning objectives with the downstream prediction consumed by an algorithm.A generic loss may not reflect how equal prediction errors perturb different decisions.
  • Budgeting predictor queries: Query-budget models optimize prediction consultations separately from accuracy, including sparse-query caching and explicit prediction costs in ski rental and Bahncard.An abstract conversion from query cost into objective units is treated separately.
  • Portfolios: Prediction portfolios select among multiple predictors under stated covering, regret, or competitive guarantees, but state-transition costs must be included when decisions carry state.Portfolio analysis therefore depends on the underlying stateful problem.
  • Uncertainty: Uncertainty-quantified predictions can provide ranges and coverage probabilities, but coverage is not a generic downstream cost bound.Independent ε-accuracy and calibrated confidence are distinct assumptions.
  • Open directions: Two directions remain incompletely resolved: proving premises for semantic predictors and reducing distribution-free coverage guarantees to downstream cost.Time-decay estimation results use a suffix-compatible oracle without proving that premise for a particular language model.

6 System-Level Implications and Composition

Learning-augmented components do not automatically compose into system guarantees because stages may alter instances, benchmarks, costs, and error sensitivity. Limited end-to-end reasoning requires explicit interface conditions, including benchmark relations, conditional guarantees, and edge-level sensitivity.

  • System-level omissions: Prediction inference, training, and sample collection are often excluded from standard competitive objectives, so reported per-request overhead may omit prediction-production costs.Cost-aware models instead expose invocation costs or query budgets explicitly.
  • System-level omissions: Component ratios alone do not determine a pipeline ratio when adjacent stages see different induced instances and offline benchmarks.Composition must relate benchmark distortion, state transitions, and error sensitivity.
  • System-level omissions: Figure 3 separates the decision path from feedback, whose signals may arrive too late for fast mechanisms but can support recalibration or retraining.The deployment accounting view distinguishes immediately observable signals from delayed outcomes.
  • Inference graphs: An inference graph is a DAG of learning-augmented components whose edges indicate outputs feeding later predictors or decision rules.Nodes declare consistency, robustness, and smoothness, while source and terminal nodes represent external predictions and actuation.
  • Inference graphs: Under additive composition with common benchmark comparison and conditional guarantees, system consistency, robustness, and smoothness are bounded by the maximum component guarantee divided by β.The bounds are c_sys ≤ max_i c_i/β, r_sys ≤ max_i r_i/β, and f_sys(η̄) ≤ max_i f_i(η̄_i)/β.
  • Cascaded composition: Cascaded composition requires edge-specific benchmark-distortion factors because earlier-stage ratios matter only when they control downstream benchmarks.Perfect component consistency therefore need not imply perfect system consistency.
  • Error propagation: Smoothness transfers only when every edge has a compatible metric, Lipschitz bound, or additive perturbation model.Without such conditions, the recursion supplies no transferred smoothness guarantee.
  • Deployment implications: System guarantees must state which instance is produced, how benchmarks relate, which costs are incurred, and which sensitivity property supports error propagation.Safety monitors and fallbacks also require observable signals and independent proofs.

7 Semantic Predictions and Large Language Models

Semantic predictors, including language models, must be converted into the task-defined prediction space before learning-augmented theorems apply. The survey therefore treats language-model guarantees as conditional on adapters, error measures, calibration, validation, and model-specific interface assumptions.

  • Prediction interfaces: Learning-augmented analyses usually assume task-defined objects such as numbers, rankings, distributions, or combinatorial structures, whereas language models may emit free-form text.An interface must map text into the theorem’s prediction space and define an error measure.
  • Prediction interfaces: Foundation models can map unstructured context to declared task objects, but their accuracy and cost should be compared with parsers, extraction systems, and other NLP models.The survey does not treat foundation models as uniquely suitable for this role.
  • Evidence boundaries: Streaming experiments using language-model implementations establish conditional-interface evidence, not an unconditional guarantee for a named model on arbitrary streams.The relevant theorem assumes a suffix-compatible heavy-hitter oracle.
  • Operational roles: A language model can serve as predictor, adapter, policy synthesizer, or explainer, with different validation and authority requirements.The relevant control point is where an unvalidated output can change state.
  • Calibration and uncertainty: Token likelihood, sampled-completion agreement, and semantic entropy are not universal certificates of task correctness.Their relationship to correctness can vary with prompts, decoding, and model versions.
  • Calibration and uncertainty: Conformal wrappers can convert outputs and calibration data into prediction sets, but coverage assumptions and downstream cost implications require separate analysis.Exchangeability underlies standard split-conformal coverage, while non-exchangeability incurs model-specific penalties.
  • Safety and failure modes: Operational responses such as abstention, review, constrained actions, or fallbacks are application dependent and do not automatically bound cost or harm.A generic safety mechanism becomes a guarantee only through problem-specific analysis.
  • Evidence boundaries: No surveyed result unconditionally verifies a particular language model over a theorem’s full instance class, and calibration alone is insufficient.Richer semantic side information requires a specified predictor class, error model, benchmark, and new analysis.

8 Open Challenges

The survey identifies open challenges in pricing prediction calls, composing interacting components, modeling policy-dependent error, and making empirical comparisons meaningful. These challenges require extending theorem statements beyond isolated components and standard objectives.

  • Predictor cost: Prediction cost is absent from the competitive ratios reviewed, motivating a declared conversion κ from predictor invocations to objective units.The proposed κ-augmented cost adds κq_A to algorithmic cost while leaving the prediction-free optimum uncharged.
  • Predictor cost: Exact multiplicative 1-consistency against an uncharged optimum is impossible when exact-prediction instances incur positive prediction cost, absent an additive term or alternative benchmark.For q_A = T, the augmented ratio gains κT/OPT(σ).
  • Composition: A fuller composition calculus must model correlated claims, policy-dependent cycles, objectives, state constraints, and limited fallback capacity.Existing sufficient conditions require benchmark decomposition, distortion factors, or metric sensitivity.
  • Endogenous error: Bounds conditional on realized error do not model how decisions change later observations, so endogenous error needs an explicit feedback or adaptation model.Performative prediction, feedback control, and strategic classification provide distinct tools but not a general consistency–robustness guarantee under policy-dependent data.
  • Empirical comparability: Comparable empirical benchmarks should report traces, shifts, error protocols, objectives, feasibility, interventions, predictor calls, latency, prediction type, trust, splits, and baselines.Such evaluations complement rather than validate universal guarantees.

9 Conclusion

The survey separates theorem-specific guarantees, construction mechanisms, matching-bound status, and empirical systems evidence. It concludes that deployment claims require explicit accounting for prediction cost, feedback, and component interfaces rather than architecture alone.

  • Synthesis: The survey records five non-exclusive construction mechanisms and an orthogonal same-model matching-bound axis, distinguishing proved frontiers, achieved upper bounds, and empirical systems evidence.Neither axis is presented as a maturity ranking.
  • Deployment implications: Systems also incur prediction cost, policy-dependent feedback, and component interactions that require explicit objective, benchmark, state, and error relations.Operational safeguards become guarantees only through problem-specific analysis.
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