Energy Preference Optimization (EPO)

Updated 20 November 2025

Energy Preference Optimization (EPO) is a framework that uses energy evaluations to guide optimization by favoring lower-energy, stable, and efficient solutions across varied domains.
EPO methodologies integrate techniques like grid search, genetic algorithms, reinforcement learning, and direct preference optimization to balance energy efficiency with performance metrics.
Empirical results highlight EPO’s effectiveness, showing significant energy savings and performance improvements in applications such as HPC scheduling, protein design, and quantum control.

Energy Preference Optimization (EPO) encompasses a class of techniques and algorithmic frameworks that optimize systems or models by leveraging preference signals derived from energy evaluations. Rather than relying on explicit labeled supervision or conventional gradient-based objectives alone, EPO utilizes the intrinsic structure of energy landscapes—be they physical potentials, power consumption models, or learned energy proxies—to guide optimization. EPO methodologies arise in diverse settings, including high-performance computing (HPC), communications networks, molecular design, protein conformational ensemble modeling, and machine learning for test-time adaptation. Core to many EPO approaches is the conversion of energy values or rankings into optimization targets, often by recasting model improvement as a direct preference problem, in which lower-energy (more stable, efficient, or physically plausible) candidates are favored, with mechanisms drawn from discrete optimization, reinforcement learning, or listwise preference modeling.

1. Formal Definitions and Mathematical Foundations

EPO frameworks are typically formulated as constrained or unconstrained optimization problems with energy serving as an explicit objective, constraint, or reward. The precise form depends on the domain of application:

Deterministic Design (HPC/Grid): The objective is to minimize total consumed energy, such as $E(f, c) = P(f, c) \times T(f, c)$ , where $P$ is power (modeled, e.g., by a CMOS-inspired cubic function of frequency $f$ and core count $c$ ), and $T$ is an SVR-predicted execution time. EPO seeks optimal $(f^*, c^*) = \arg\min_{f, c} E(f, c)$ subject to architectural and QoS constraints (Silva et al., 2018, Vavřík et al., 2015).
Multi-objective Scheduling: EPO addresses trade-offs between energy $E(x)$ and other system characteristics (overhead, throughput) through Pareto optimization: $\min F(x) = (E(x), O(x))$ , with $x$ a vector of scheduler parameters, and searches for non-dominated solutions—often using evolutionary or genetic algorithms (Kell et al., 2019).
Preference-Based Learning: Here, energy-driven preferences induce pairwise or listwise rankings, framing the optimization as Direct Preference Optimization (DPO) where the loss reflects the probability that a lower-energy state (winner) should be favored over a higher-energy state (loser), formalized as $L_{\text{DPO}}(\theta) = -\mathbb{E}_{x_w, x_l} \left[ \log \sigma(\beta[\log p_\theta(x_w)/p_\text{ref}(x_w) - \log p_\theta(x_l)/p_\text{ref}(x_l)]) \right]$ , with $\sigma$ the logistic sigmoid and $\beta$ controlling sharpness (Zhou et al., 25 Mar 2024, Rong et al., 11 Jun 2025, Sun et al., 13 Nov 2025).
Reinforcement Learning (RL): EPO is embedded within the reward structure of RL agents with composite objectives, e.g., $J(\pi) = \mathbb{E}_{s,a\sim\pi} [\omega_{\mathrm{perf}}\,G_{\mathrm{perf}}(s,a) + \omega_{\mathrm{power}}\,P_{\mathrm{gain}}(s,a)]$ , where $G_{\mathrm{perf}}$ and $P_{\mathrm{gain}}$ measure throughput improvement and power-saving, respectively (Ntassah et al., 20 Apr 2025).

In physical and generative modeling, EPO also appears in conjunction with stochastic differential equation (SDE) sampling, energy-based models, and explicit energy constraint losses for alignment with experimental measures (e.g., $\Delta\Delta G$ in protein design).

2. Algorithmic Mechanisms and Model Architectures

The operationalization of EPO varies according to the underlying optimization landscape, data availability, and computational constraints:

Brute-Force or Enumerative Strategies: In low-dimensional HPC or scheduling, EPO employs exhaustive grid search across CPU frequencies and core counts (Silva et al., 2018).
Genetic & Evolutionary Algorithms: Multi-objective EPO often utilizes NSGA-II for efficient exploration of high-dimensional parameter spaces, enabling dense sampling of the Pareto frontier (Kell et al., 2019).
Reinforcement Learning (PPO-EPO): In cellular networks, PPO-driven EPO observes per-cell resource and interference metrics, taking on/off actions, balancing energy and performance via carefully weighted reward signals and constrained policy networks (MLPs, GAE, gradient clipping) (Ntassah et al., 20 Apr 2025).
Direct Preference Optimization (DPO): EPO frequently leverages DPO frameworks, converting energy differences into logistic preference probabilities either pairwise or listwise. Residue-level or atom-level decomposition is used in biophysical applications, often with auxiliary mechanisms like gradient surgery (PCGrad) to avoid conflicting updates when optimizing multiple energy terms (e.g., attraction versus repulsion in antibody design) (Zhou et al., 25 Mar 2024, Rong et al., 11 Jun 2025).
Online Listwise Preference Optimization: In protein conformational ensemble generation, EPO refines pretrained flow-matching or diffusion models with listwise Plackett–Luce losses, ranking sampled conformations by energy and backpropagating per-timestep MSE differences (upper bounding intractable pathwise log-probabilities) (Sun et al., 13 Nov 2025).
Closed- and Open-Loop Quantum Control: EPO is instantiated in quantum pulse engineering via both gradient-based (EO-GRAPE) and RL (EO-DRLPE) algorithms, directly embedding the derived energy cost as a term in the total loss/reward (Fauquenot et al., 10 Nov 2024).

3. Applications Across Domains

EPO is adapted to a variety of domains, each with its own problem-specific constraints and objectives:

Domain	Formulation	Key Metrics/Objectives
HPC & Grid Scheduling	Discrete energy minimization, Pareto	Total energy, overhead, precision
Telecommunication (O-RAN)	RL reward optimization (PPO-EPO)	Energy efficiency, throughput, CDF
Molecular/Protein Design	DPO with residue-level energy, listwise	Total/binding energy, $\Delta\Delta G$
Ensemble Generation	Listwise energy ranking post-SDE	JSD, RMSD, ensemble diversity
Quantum Control	Weighted sum (fidelity, energy)	Gate infidelity, normalized energy
Test-Time Adaptation	Sampling-free DPO for EBMs	Accuracy, calibration error, FLOPs

EPO yields improved energy efficiency, model calibration, and physically meaningful solutions while accommodating trade-offs with other system objectives such as throughput, overhead, or biological binding affinity.

4. Empirical Results and Comparative Performance

Empirical kinematics of EPO across settings include:

PPO-EPO in O-RAN: Attains up to 30% average energy-efficiency improvement over random cell-selection, ~15% over SARSA; maintains median downlink throughput (≈42 Mbps vs. 35 Mbps for SARSA), and under interference, provides <5% throughput degradation versus >20% for random selection (Ntassah et al., 20 Apr 2025).
Single-Node HPC: EPO achieves average energy savings of ≈6% over ondemand-best (Linux DVFS), up to 23% for selected applications, and 14× less energy than the worst-case (user-chosen) configuration (Silva et al., 2018).
Multi-objective Scheduling: NSGA-II EPO reduces HTC-Sim energy by ∼36% with <2% increase in overhead; weighted-sum selection along the Pareto front enables tailored energy–overhead trade-offs (Kell et al., 2019).
Antibody and Protein Design: EPO-based DPO (AbDPO, EnerBridge-DPO) increases the fraction of designs passing biophysical energy and binding constraints, reduces residue clash artifacts, and achieves comparable or superior metrics (e.g., CDR E_total, $\Delta G$ ) to prior state-of-the-art approaches (Zhou et al., 25 Mar 2024, Rong et al., 11 Jun 2025).
Ensemble Generation: EPO-listwise finetuning establishes new state-of-the-art metrics (e.g., JSD on molecular features, RMSD, RMSF) on tetrapeptides, ATLAS, and fast-folding protein benchmarks without additional MD simulation (Sun et al., 13 Nov 2025).
Quantum Control: Reveals explicit Pareto front between fidelity and energetic cost; EO-GRAPE outperforms RL and hybrid warm-starts in low-noise regimes—demonstrating the inherent trade-off and the correlation between geometric path length and energetic expenditure (Fauquenot et al., 10 Nov 2024).
Test-Time Adaptation: EPOTTA’s EPO objective (sampling-free DPO) achieves strong accuracy and calibration while requiring ∼6× fewer FLOPs than SGLD-based adaptation (TEA), with modest memory usage (Han et al., 26 May 2025).

5. Limitations, Theoretical Considerations, and Extensions

EPO methods are subject to a number of practical and theoretical limitations:

Domain-Specific Modeling: Power and performance models must be retrained for each application/hardware combination; accurate energy proxies are essential for stability (Silva et al., 2018, Kell et al., 2019).
Preference Quality: The efficacy of preference-based optimization depends on the fidelity of energy rankings. In protein engineering, poor preference pair sampling or model bias in likelihood-based energies can impair calibration to experimental outcomes (Zhou et al., 25 Mar 2024, Rong et al., 11 Jun 2025).
No Guarantees of Global Optimality: While Pareto front identification and DPO provide landscape coverage and robustness, there are no theoretical guarantees of convergence to the true Boltzmann distribution in high-dimensional generative models (Sun et al., 13 Nov 2025).
Computational Cost: EPO in large-scale models (e.g., protein ensemble generation, RL in telecommunication) incurs significant computation; practical refinements include LoRA fine-tuning, SDE approximations, or adapter-based architectures (Sun et al., 13 Nov 2025, Rong et al., 11 Jun 2025).
Softness of Preference (Listwise vs. Pairwise): Listwise EPO preserves ensemble diversity better than binary or pairwise ranking, aligning with the properties of physical distributions with rare or functionally relevant rare states (Sun et al., 13 Nov 2025).
Extension Potential: EPO can be directly transplanted to other science and engineering domains with continuous or discrete energy-like observables, including enzyme redesign, control in edge networks, or constrained scheduling under soft real-time requirements.

A plausible implication is that as energy-based and preference-driven learning frameworks mature—especially in conjunction with generative models and RL—the role of EPO strategies is likely to increase in both theoretical and applied research optimizing for system-level performance under physically realistic constraints.