Performance-Aware Cost (PAC) Optimization

• Performance-Aware Cost (PAC) is a framework that maps system configurations to multi-dimensional cost vectors, identifying Pareto optimal solutions.
• PAC methodologies integrate software autotuning, cloud scheduling, and adaptive inference to optimize resource allocation and performance trade-offs.
• Empirical results show that PAC-guided approaches achieve significant cost reductions and performance gains by systematically pruning suboptimal configurations.

Performance-Aware Cost (PAC) quantifies and optimizes the trade-off between resource expenditure and performance in computational systems. The concept formalizes evaluation and search where multiple metrics—such as execution time, energy, monetary cost, memory, or prediction risk—are simultaneously tracked and operational decisions or system designs are guided by their Pareto frontier or explicit cost-performance objectives. PAC methodologies have been developed and empirically validated across software autotuning, systems scheduling, machine learning model orchestration, protocol analysis, classifier evaluation, and adaptive inference.

1. Formal Definitions and Core Mathematical Structure

The defining mathematical principle of PAC is the multi-objective mapping from a system configuration to a vector of quantifiable costs, seeking simultaneous minimization in the Pareto sense. For a configuration $x$ (representing, e.g., code, flags, hardware, input), the multidimensional cost is

$$C(x) = \bigl(T(x),\,E(x),\,S(x),\,M(x),\,\dots\bigr),$$

where typical components are execution time $T(x)$, energy $E(x)$, code size $S(x)$, and memory footprint $M(x)$; other application-dependent metrics (accuracy loss, failure rate, storage, etc.) may be included. The optimization target is the Pareto frontier

$$\mathcal{P} = \left\{x \mid \nexists y: C(y) \le C(x),\ C(y) \ne C(x)\right\}.$$

Users may scalarize via application-specific weights $\alpha,\beta,\gamma$ in loss functions $\mathcal{L}_{x} = \alpha T(x) + \beta E(x) + \dots$, or utility functions $U_x = S_x/(C_x)^\gamma$ (Fursin et al., 2015, Nassereldine et al., 2023).

In system benchmarking and cloud scheduling, PAC curves are computed as the set of $(C_{s,k}, T_{s,k})$ pairs where $C_{s,k} = r_{s,k}\cdot T_{s,k}$ for execution time $T_{s,k}$ and cost rate $r_{s,k}$ of system $s$ under configuration $k$ (Nassereldine et al., 2023). For classifier evaluation under asymmetric misclassification costs and operational constraints such as minimum precision and upper capacity, the PAC metric corresponds to the partial volume over the feasible ROC region (Partial VOROS) as an integral of cost-monotone area measures (Ratigan et al., 21 Oct 2025).

2. PAC Methodologies Across Domains

a. Software Autotuning and Code Optimization

All candidate implementations are minimally instrumented as "computational species," each exposing its optimization choices, feature vectors, and cost vector. Iterative autotuning—random or predictive—systematically explores configurations, reporting observed cost vectors to a central repository. Pareto filtering maintains the current frontier per species/platform/dataset; irrelevant or dominated records are pruned. Predictive analytics cluster optimizations and correlate static/dynamic features with frontier memberships to guide further search or to drive compiler improvements (Fursin et al., 2015).

b. System Scheduling and Cloud Cost-Benefit Analysis

The PAC curve is employed to expose the performance-cost trade-off for any application across multiple hardware environments and configurations. Minimal finger-printing (brief, partial runs with selective profiling) combined with learned regression/classification models predicts the whole cost-performance trade-off space, accounting for environmental factors such as multi-tenant interference (Nassereldine et al., 2023).

c. Concurrent/Distributed Protocol Analysis

PAC in this context refers to symbolic and compositional cost tracking for protocols, with explicit send, receive, and compute cost annotations in session types. Cost equations are derived via the operational semantics and solved either analytically or via external tools, yielding upper bounds on protocol end-to-end costs (Castro-Perez et al., 2020).

d. Classifier Evaluation with Deployment Constraints

The Partial VOROS metric restricts ROC analysis to classifier configurations satisfying specified minimum precision and maximum positive prediction rate and explicitly integrates over user-specified cost asymmetries. The area of "lesser classifiers" beneath each operating point quantifies its relative merit with respect to the deployment cost structure, ensuring cost-monotonicity and standard ROC dominance ordering (Ratigan et al., 21 Oct 2025).

e. Adaptive Inference and Reasoning Systems

PAC in adaptive inference selects dynamic routing or switching strategies (e.g., LLM self-answering vs. tool-calling, or high-accuracy vs. low-cost model selection) to guarantee user-specified maximal performance loss, rigorously upper-bounded with statistical confidence. Techniques utilize uncertainty scores, upper confidence bounds, and threshold selection for switching decisions, with savings in computational budget under explicit risk controls (Zeng et al., 10 Oct 2025, Qian et al., 9 Oct 2025).

3. Data Collection, Model Training, and Frontier Pruning

PAC-based frameworks typically maintain large datasets mapping configuration or decision variables to cost vectors. Data flows are:

• Crowdsourced measurement: Distributed or volunteer machines run autotuning jobs, each submitting JSON-encoded reports of configuration, environment, features, and measured costs.
• Storage and indexing: All records are stored for indexed retrieval and filtering, with Hadoop or similar large-scale backends (Fursin et al., 2015).
• Frontier updates: Incoming data is compared against the existing Pareto frontier. Dominated points are discarded, dominant ones replace predecessors, and incomparable points expand the frontier.
• Clustering: Redundant optimizations are pruned using meta-flags or minimal sets of influential features; large-scale experiments yield clusters of distinct optimization behaviors.
• Predictive analytics: Regression/classification models (e.g., XGBoost, SVM, decision trees) are trained on observed features versus cluster memberships for predicting cost-performance profiles or best optimization actions (Nassereldine et al., 2023).

4. Application Case Studies and Empirical Results

Table: Selected PAC instantiations and empirical results

Domain	Implementation/Metric	Salient Outcome
Software autotuning	Computational species, cM repository	79 GCC optimization clusters cover 285 species, major speedup gains (Fursin et al., 2015)
System scheduling	Multi-system PAC curves	3-config fingerprint yields <23% SMAPE error in predicting trade-off
Protocols	Session-type cost formulas	<20% error in predicted upper-bound for protocol runtime (Castro-Perez et al., 2020)
Classifier eval.	Partial VOROS metric	Achieves lowest cost in high-precision, constrained deployment (Ratigan et al., 21 Oct 2025)
LLM orchestration	Cost-gated RL (xRouter)	Sits close to empirical Pareto, 30%+ cost reduction at fixed accuracy (Qian et al., 9 Oct 2025)
Adaptive inference	PAC reasoning (UCB)	<user-specified error, 23–40% token savings, rigorous PAC guarantee (Zeng et al., 10 Oct 2025)

In practical terms, PAC-guided approaches consistently identify operationally superior configurations, whether for software/hardware co-design, scheduler resource allocation, protocol optimization, classifier deployment, or AI system orchestration.

5. Analytical Extensions, Generalizations, and Open Challenges

PAC frameworks are designed for extensibility in cost dimensions and domain adaptation:

• Metric augmentation: New metrics (e.g., IO bandwidth, thermal envelope, reliability quantiles) can be integrated with no algorithmic change—only higher-dimensional Pareto frontiers (Fursin et al., 2015).
• Hardware/platform neutrality: Wrappers and annotation systems allow ready extension to new platforms (e.g., GPUs, FPGAs, domain-specific accelerators).
• Fine-grained optimization: Automated code extraction, IDE/compiler plugins, and deep-feature analytics seek to reduce manual effort and improve coverage of the design space.
• Theory and automation trade-off: Negative results, feature confluence, and non-monotonic error surfaces often require hand-inspection; end-to-end automation remains an open research direction.
• Scalability: Multi-objective search and model training in high dimensions increase computational complexity and expand the Pareto set; hybrid random/guided/active search is under continued paper (Fursin et al., 2015, Nassereldine et al., 2023).
• Statistical risk control: PAC-reasoning introduces calibrated uncertainty-based upper confidence bounds, offering PAC-style guarantees for adaptive inference under resource constraints (Zeng et al., 10 Oct 2025).

6. Impact, Community Infrastructure, and Future Directions

Public repositories (c-mind.org/repo, cknowledge.org) have made PAC benchmarking, data, and model artifacts openly available, fostering reproducible science and collaborative development. The community maintains an evolving benchmark suite and optimization knowledge base, with mechanisms for classification, correction, and extension. The modularity of PAC methodology—unifying measurement, filtering, learning, and deployment—positions it as a foundational paradigm for data-driven software engineering and operational decision making in complex, cost-aware environments.

Continued progress in PAC research targets automated feature extraction, more expressive protocol cost models (e.g., dynamic and probabilistic annotations), scalable search, and seamless system integration via advanced developer tools. The shift towards natural science paradigms, emphasizing continuous, experimental, and Pareto-tracking inquiry, underpins the role of PAC as a meta-framework for the empirical optimization of digital and AI systems (Fursin et al., 2015, Nassereldine et al., 2023, Ajasa et al., 21 Oct 2025, Zeng et al., 10 Oct 2025, Castro-Perez et al., 2020, Ratigan et al., 21 Oct 2025).