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The Operable Pareto Front: Distilling Offline Search into Run-Time Control for Multi-Objective UAV Edge-Computing Scheduling

Qiao Liao, Zhiyong Feng, Bin Wu, Guodong Fan

arXiv:2609.17992v1cs.NIcs.LG

TL;DR

UAV-MEC fleets must trade delay against energy, but schedules are often committed to one trade-off and predicted energy use. PrefDT is an offline-trained, preference-conditioned scheduler that uses distilled flight logs to serve requested trade-offs at run time. Across 26 method variants it achieves the best learned trade-off curve and stays within 0.6% of its energy budget after propulsion cost rises by half mid-flight.

  • Problem

    Long-term energy constraints couple scheduling decisions across slots, while a Lagrangian treatment bakes one budget into training and requires retraining for another.

    Source: E. Constrained multi-objective… · p. 4

  • Method

    PrefDT uses preference-annotated flights distilled from a searched control rule to train a frozen model that accepts the requested trade-off at run time.

    Source: §I · p. 2, §VI · p. 13

  • Results

    Across 26 method variants, PrefDT produces the best trade-off curve of any learned method and stays within 0.6% of its energy budget when propulsion cost rises by half mid-flight.

    Source: §I · p. 3, §VI · p. 13

  • Takeaways & Limitations

    A single frozen model can serve requested trade-offs at run time while honoring a revisable energy budget against actual consumption.

    Source: §VI · p. 13

    The results are measured in one physics-based simulator family with i.i.d. arrival processes, and the uplink bandwidth is uncontended by construction.

    Source: §VI · p. 13

Abstract

from arXiv · show

A UAV mobile edge computing (MEC) fleet trades energy against delay, and its schedules form a Pareto front; we call a scheduler operable when the fleet can be asked for any point on that front at run time. We propose PrefDT, to the best of our knowledge the first preference-conditioned Decision Transformer for the problem of joint trajectory, association and offloading scheduling. Its idea comes from language modeling: we hand the model the desired trade-off as an input, such that a single model only needs to be trained once offline to return any desired point on the curve in one rollout. The fleet's state is summarized by attention pooling with a per-user bypass, so the scheduler keeps working when user reports are lost. The energy target is a running budget decremented by what the fleet actually spends. As a result, when wind or load pushes consumption off the plan, the policy can track the difference and hold its budget. Because no corpus of preference-labeled flights exists, we design a distillation pipeline and build the corpus by ourselves. In simulation against 26 method variants, PrefDT produces the best trade-off curve of any learned method and holds its energy budget to within 0.6% when propulsion cost rises by half in mid-flight.

I. INTRODUCTION

UAV-MEC scheduling must balance delay and energy while letting fleets change that balance during a mission, track actual energy use, and continue when user reports are lost. PrefDT addresses these needs with one offline-trained, preference-conditioned scheduler and a corpus distilled from searched flights.

I. INTRODUCTION

  • Existing optimization and learned schedulers commit to a trade-off at solve or training time, while population methods return a fixed menu rather than a continuum.Changing the trade-off can therefore require another solve, training run, or search.Source: §I · p. 1
  • An operable scheduler must accept a requested trade-off at run time, honor an energy budget against actual consumption, and accept a mid-flight budget revision as a single new total.The paper defines operability through these three requirements and makes the term measurable in Sec. IV-C.Source: §I · pp. 1–2
  • A pooled state summary handles changing user counts, while a bypass routes each user's raw token to that user's own association and offloading heads.Because the summary works on any subset of users, a lost report leaves a smaller input and does not require retraining.Source: §I · p. 2
  • The goal vector gives delay and energy separate entries, and its energy entry is decremented each slot by actual consumption so the policy reads the remaining budget.A mid-flight budget revision overwrites that entry.Source: §I · p. 2
  • The distillation pipeline searches a compact control rule, matches sampled preferences to archived flights by realized delay–energy share, and records those flights with realized-trade-off labels.It oversamples extreme front members to counter imitation's regression toward the behavioral mean; the corpus costs one offline search.Source: §I · p. 2
  • PrefDT supplies the desired trade-off as an inference-time input to one frozen model, so a new setting needs one rollout rather than another solve, search, or training run.The model is trained offline from preference-annotated logs and is not updated at run time.Source: §I · p. 2
  • Across 26 method variants, PrefDT produces the best trade-off curve of any learned method; its 0.41-second rollout is 620–2400× faster than a re-solve or retraining, and it stays within 0.6% of its energy budget after a 50% propulsion-cost rise.The budget result is measured when the cost change occurs mid-flight.Source: §I · p. 3

II. SYSTEM MODEL AND PROBLEM FORMULATION

The system model places UAV edge servers over ground users and jointly schedules flight, association, and offloading. It uses a time-varying active user set and a probabilistic air–ground channel model with per-user bandwidth.

A. Network model and decision variables

  • The modeled fleet has M rotary-wing UAV edge servers flying at fixed altitude over a square service area for U ground users across T slots.The physical models follow prior multi-UAV MEC work so baselines share an identical environment.Source: A. Network model and decision variables · p. 3, §II · p. 3
  • Each slot's active set contains 4–8 users selected from the pool, and each active user carries a task with probability pa.The active set changes in cardinality and membership over time.Source: A. Network model and decision variables · p. 3
  • Each UAV's per-slot flight control is bounded by a maximum step length, with heading in [0, 2π) and speed equal to step length divided by slot duration.The passage defines the motion variables but does not provide their numerical limits.Source: A. Network model and decision variables · p. 3
  • The scheduler jointly chooses flight controls, binary user–UAV association, and each associated user's continuous task-offloading fraction.Each active user can be served by at most one UAV; edge compute is shared equally among users served by a UAV.Source: A. Network model and decision variables · p. 3

B. Air–ground channel

  • The air–ground channel uses elevation-dependent LoS probability to mix LoS and NLoS states, with slot-level quasistatic channels and state-dependent attenuation, shadowing, and fading.The adopted channel model and urban parameters follow.Source: B. Air–ground channel · p. 3
  • The modeled uplink uses a 2 GHz carrier, B=1 MHz per user, Pu=0.1 W, and σ2=−110 dBm.Each served user has its own channel; bandwidth contention among users on one UAV is omitted, leaving shared edge compute as the cost of adding a user.Source: B. Air–ground channel · p. 3

C. Task and computation model

The task model assigns each arriving task an input size, computing density, and deadline, and splits execution between local and edge processing. The energy model combines UAV propulsion and edge-computation costs.

C. Task and computation model

  • Each task is specified by input size Du, computing density Cu, and deadline τu^dl, with the model holding Cu at one value in its instantiation.The offloaded and local portions execute in parallel on the edge server and user CPU, respectively.Source: C. Task and computation model · p. 3
  • Tasks finish within their arrival slot without cross-slot queueing, and missed deadlines count as violations in the delay increment.The delay increment sums completion times over active users and adds penalty χ per violation, sized not to dominate the controllable objective.Source: C. Task and computation model · p. 3

D. Energy model

  • The propulsion model retains the parasite v^3 term and has an interior minimum at 8.4 m/s; hovering costs 25% more and flying at 30 m/s costs 4.8× more.The passage states that truncating the model after two terms would make hovering and cruising nearly isoenergetic, eliminating the energy–delay tension.Source: D. Energy model · p. 3
  • Edge-computation energy follows a cubic power law, with per-task energy κc fm,u(t)^2 ρu(t) Du Cu.The per-slot energy increment sums flight power over the slot and edge-computation energy across each UAV's served users; user-side energy is not an objective.Source: D. Energy model · p. 3

E. Constrained multi-objective scheduling problem

The scheduling formulation is a constrained, non-convex multi-objective problem whose delay and energy objectives conflict. The paper recasts it as a multi-objective MDP and seeks one conditional policy that approaches Pareto-optimal returns across attainable preferences.

E. Constrained multi-objective scheduling problem

  • P1 is a non-convex mixed-integer nonlinear program with motion, collision, association, offloading, compute-capacity, and long-term energy constraints; even scalarized instances are NP-hard.Continuous flight and offloading decisions couple with binary association through the non-convex rate and non-monotone propulsion curve.Source: E. Constrained multi-objective… · p. 4
  • The long-term energy constraint C6 couples slots through cumulative consumption, so honoring the budget requires tracking across the horizon; a Lagrangian treatment instead bakes one budget into training.Constraints C1–C5 bind slot by slot, while C6 spans the horizon.Source: E. Constrained multi-objective… · p. 4
  • Because delay and energy conflict, P1 has a Pareto set, and the goal is one policy that can reach any point on it when requested.The paper negates the objectives and defines dominance over the resulting vector returns.Source: E. Constrained multi-objective… · p. 4

F. Multi-objective MDP reformulation

  • The MDP state includes UAV and active-user indicators, its action is the joint scheduling decision, and its vector reward is the negative delay and energy increment.The finite-horizon MDP uses γ=1, and its expected vector return equals the negative total delay and energy.Source: F. Multi-objective MDP reformulation · p. 4
  • A single conditional policy takes a preference over the two objectives and seeks Pareto-optimal returns at every attainable preference, rather than solving one scalarized instance per preference.Preferences beyond the physically achievable front saturate rather than producing more extreme outcomes; the stated scope excludes an aliasing regime that begins at three objectives.Source: F. Multi-objective MDP reformulation · p. 4

G. Why not scalarize first

PrefDT avoids linear scalarization by imitating preference-labeled behavior, while its setting is supplied at run time to a frozen model. Its state encoder combines a fleet-level user summary with a direct per-user path, allowing decisions for changing active sets.

G. Why not scalarize first

  • In this non-convex scheduling problem, linear scalarization cannot reach unsupported Pareto-optimal points; preference-labeled imitation instead limits reachability by corpus coverage.The offline pipeline removes live interaction at deployment, not the need for a competent teacher, whose search costs 606,000 slots.Source: G. Why not scalarize first · p. 4

III. THE PROPOSED PREFDT SCHEDULER

  • The requested setting is read at run time rather than compiled into the training objective, and the two-scale pipeline ends in a frozen artifact.The figure contrasts one-time offline corpus creation and training with the per-slot run-time loop.Source: §III · p. 4, Figure 1 · p. 5

III-A POOLING + BYPASS

  • Each UAV pools active users into a fixed-width summary, while each user’s own features bypass pooling to inform that user’s decisions.The summary is symmetric and loses user identity, so the per-user path supplies member-specific features directly to the decision heads.Source: §III-A · p. 5, A. The state encoder: tokens, pooling,… · p. 5

A. The state encoder: tokens, pooling, and the per-user path

  • The encoder accepts changing active-set sizes without retraining, and lost reports leave a smaller set rather than requiring substitute values.It continues to produce decisions for the remaining users.Source: A. The state encoder: tokens, pooling,… · p. 5

B. The return channel: the vector return-to-go, its decrement, and the sequence model

The return channel represents each objective separately, carrying both the requested trade-off and a revisable energy budget through the sequence model. The return-to-go is decremented by realized rewards, so the energy entry tracks what remains after actual consumption.

B. The return channel: the vector return-to-go, its decrement, and the sequence model

  • A vector return-to-go gives each objective its own remaining return, allowing the energy entry to start at the requested budget and decrease with actual consumption.The entries are rescaled by fixed per-objective constants archived for both training and rollout.Source: B. The return channel: the vector… · p. 6
  • The preference is concatenated to state and action tokens and element-wise weights normalized return-to-go, making it part of every position’s representation.The preference-conditioned stream is processed by a causal GPT over a context of 20 slots.Source: B. The return channel: the vector… · p. 6
  • Training uses imitation loss combining L2 losses for continuous actions with cross-entropy for per-user association, equally weighted.The policy head is deterministic by default; sampling association is an inference-time option without refitting parameters.Source: B. The return channel: the vector… · p. 6
  • The energy return-to-go is decremented by realized reward each slot, and revising the total budget requires only overwriting its energy entry.The energy entry represents the budget not yet spent, up to the fixed scale.Source: B. The return channel: the vector… · pp. 6–7
  • A scalar utility cannot identify a unique front point with three or more objectives or carry a budget in joules, whereas the vector form does both across objective counts.The vector decrement also provides per-objective progress rather than aggregate progress.Source: B. The return channel: the vector… · pp. 6–7

C. The distillation pipeline: corpus construction and inference

Because preference-labeled scheduling flights are unavailable, the paper constructs a corpus from a searched teacher and trains a model by imitation. At inference, calibrated settings initialize the return target, which is carried through the flight and can accept a revised energy budget.

C. The distillation pipeline: corpus construction and inference

  • The corpus must be produced because no archive of scheduling flights labels each run with the trade-off it achieved.The assignment of flights to settings determines what each setting means.Source: C. The distillation pipeline: corpus… · p. 7
  • The teacher is a searched physical rule family selected to sweep the front through partial offloading while holding speed at the propulsion power minimum.Each setting is paired with the member whose realized cost composition matches it, and settings outside the family’s band are rejected.Source: C. The distillation pipeline: corpus… · p. 7
  • 50,000 preference-annotated trajectories are generated by sampling preferences, matching each to the nearest archive member by realized return share, and rolling it out.Sampling emphasizes low-delay extremes and mixes archive and scripted-heuristic rollouts in an 80/20 ratio.Source: C. The distillation pipeline: corpus… · p. 7
  • A monotone remap carries an abstract setting onto the measured non-dominated front of the trained model without changing its weights or conditioner.The calibrated setting axis makes distinct settings name distinct attainable outcomes in order.Source: C. The distillation pipeline: corpus… · p. 7
  • At rollout, a conditioner initializes the return target, which is decremented each slot; a requested energy budget can replace its energy entry and be revised in flight.A K-point front requires KT forward passes with one frozen policy and no further search.Source: C. The distillation pipeline: corpus… · pp. 7–8

A. Scenario

The evaluation uses a shared simulated UAV MEC environment and identical seeds across methods, except for the specified degradation study.

A. Scenario

  • The simulation has two UAVs at 100 m over a 1000×1000 m area, serving ten users with four to eight active per slot.Episodes run for 100 slots of one second each.Source: A. Scenario · p. 8
  • The environment models tasks, deadlines, compute rates, partial offloading, rotary-wing propulsion, and a probabilistic LoS air–ground channel.The model’s constants are listed in Appendix A.Source: A. Scenario · p. 8
  • All methods use identical evaluation seeds, except the degradation study, which adds a mid-episode propulsion multiplier.The multiplier is pinned so it cannot perturb other factors.Source: A. Scenario · p. 8

B. Methods under comparison: three declared classes

The comparison set groups 26 variants into three declared classes with differing access assumptions and roles. The section also specifies front-quality and preference-following metrics, along with experimental controls.

B. Methods under comparison: three declared classes

C. Metrics and protocol

  • HV and IGD measure front quality; setting-following uses rank correlation and reach jointly, requiring near-perfect ordering over at least 80% of the teacher span (493 s).Source: C. Metrics and protocol · p. 8
  • Inferential comparisons use 100 paired seeds and exact two-sided Wilcoxon signed-rank tests, with bootstrap confidence intervals for relative effects.Source: C. Metrics and protocol · p. 9

D. Experiment configurations

  • The protocol freezes checkpoints, fixes other factors in one-component ablations, separates calibration and evaluation seeds, and checks exact simulator equality at degradation multiplier 1.0.Source: D. Experiment configurations · p. 9

V. EXPERIMENTAL EVALUATION

Across the shared-protocol comparison, PrefDT produces the best trade-off curve of any learned method and is the only learned method on its shipped corpus to clear both setting-order and reach criteria. It also tracks energy consumption through a mid-flight propulsion-cost increase, while budget revisions follow supported conditions and physical limits.

A. Front quality, fidelity, and reach: comparing the field and selecting from it

  • PrefDT produces the best trade-off curve of any learned method and is the only learned method on its shipped corpus to clear both clauses of the pre-registered criterion.The criterion jointly reads setting–outcome order and reach; Table II reports front quality, fidelity, reach, and each method’s criterion verdict.Source: A. Front quality, fidelity, and reach:… · p. 9, Table II · p. 9
  • On the same hundred seeds, PrefDT scores 90.28 against PEDA’s 82.87, while PEDA’s setting fidelity is |ρ|=0.76 over 398 s.Adding the pooled encoder without the per-user path recovers 1.31 HV; the remaining 6.10 is attributed to the per-user bypass isolated in Table VI.Source: A. Front quality, fidelity, and reach:… · p. 10
  • PrefDT at 101 settings reaches 99.82 HV, 99.7% of the strongest teacher’s 100.10 HV, while the teacher has no fidelity and requires a new search for another point.Both are evaluated against a shared reference over 100 paired seeds; the teacher’s 101-member population uses about 2,000 policy evaluations.Source: A. Front quality, fidelity, and reach:… · p. 10, Table III · p. 10
  • The solver comparison is limited to ten seeds because an n=100 sweep costs 150–200 hours of single-core compute per solver.On those paired seeds, SCA-MPC leads PrefDT by 0.67 and the SCA oracle by 0.64; the comparison is not statistically decisive (p=0.16, 95% CI [−0.07, +1.36]).Source: A. Front quality, fidelity, and reach:… · p. 10
  • The 92.44-HV ablation reaches high front quality but has fidelity 0.643; three configurations have higher front quality, yet their advantages occupy a narrow 0.14-HV band.The full-information oracle adds only 0.11 HV over the ten-parameter rule, leaving setting order and reach to distinguish configurations.Source: A. Front quality, fidelity, and reach:… · pp. 9–10

B. Operability: setting fidelity, budget tracking, and mid-episode revision

  • Under a mid-flight 50% propulsion-cost increase, PrefDT finishes 0.6% over budget without re-issue, versus 17% for the fixed rule, which violates on every episode.With unchanged physics, the budget is followed without overrun; re-issuing the same total is exact to floating point, while below-floor revisions are ignored rather than pursued.Source: B. Operability: setting fidelity,… · pp. 10–11, Figure 2 · p. 11

C. What a new trade-off costs: one rollout against a re-solve, a re-search, and a retraining

The cost analysis compares a frozen-model rollout with re-solving, re-searching, and retraining for new trade-offs. Ablations show how the corpus and design choices affect front quality and whether settings are followed.

C. What a new trade-off costs: one rollout against a re-solve, a re-search, and a retraining

  • 0.41 s per frozen-model rollout is 620–830× cheaper than the solvers per setting, while retraining costs 2,400× the rollout.A 21-point front takes 8.6 s of rollouts, versus 5.8 hours of retraining and two hours of re-solving per evaluation seed.Source: C. What a new trade-off costs: one… · p. 11
  • Offline distillation uses stored trajectories, zero environment steps, and 40,000 gradient steps; runtime needs one forward pass per slot.The teacher searches 606,000 slots and the scalarized learner uses 2M environment steps per setting; the search cost is paid before a trade-off is requested.Source: C. What a new trade-off costs: one… · p. 11

D. Attribution by ablation: corpus, encoder, return channel, pipeline

  • The archive corpus improves front quality by 8.42 HV, more than any architectural choice, by preserving the teacher’s propulsion-power-minimum operating point.The figure shows propulsion power against flight speed and compares realized mean speed against the requested setting for PrefDT and ω-conditioned IQL trained on the same archive corpus.Source: D. Attribution by ablation: corpus,… · p. 12, Figure 3 · p. 12
  • The ablation pipeline progresses from 98.65 for the archive-corpus model to 99.04 with quadratic conditioning and 99.47 for the shipped model.Corner emphasis buys the front’s corner at fidelity 0.895; physics features then restore fidelity.Source: D. Attribution by ablation: corpus,… · p. 12
  • Removing the preference token raises hypervolume above the unablated configuration while failing both setting-related clauses; front quality alone can therefore select a model that ignores requests.The ablations also show that the per-user bypass matters: removing it lowers front quality, fidelity, and reach together.Source: D. Attribution by ablation: corpus,… · p. 12

E. Deployment: what the link need not guarantee, and what scale does not widen

The deployment evaluation shows that PrefDT tolerates dropped reports and transport delays within a slot, but requires a current-slot snapshot and remains bounded by its trained operating point. The conclusion reports the strongest learned-method trade-off curve and budget tracking under a mid-flight physics change.

E. Deployment: what the link need not guarantee, and what scale does not widen

  • At 40% report loss, 71.1% of PrefDT’s front survives without retraining or special handling, versus 60.8% for the per-user rule.At 5% report loss, 96.7% survives; the pooled summary accepts any subset of active users without inventing substitute values.Source: E. Deployment: what the link need not… · p. 12
  • At 40% report loss, substituting each user’s last received report raises PrefDT retention to 80.0%, while the same substitution lowers the per-user rule’s retention by 3.3 points.Across 5, 10, 20 and 40% loss, the change lifts PrefDT retention by 1.0, 2.1, 4.3 and 8.9 points, respectively.Source: E. Deployment: what the link need not… · pp. 12–13
  • At fleet sizes M=2, 4 and 8, retrained models retain 78–80% of the teacher ratio, and per-slot decisions take under 2% of a slot.The encoder’s parameter shapes bind fleet size, so serving a different size requires retraining.Source: E. Deployment: what the link need not… · p. 13

F. The boundaries: state synchronization, and the trained operating point

  • A snapshot displaced by one slot leaves 49.5% retention, and displacement up to five slots stays between 49.0 and 50.0%, making current-slot state synchronization a boundary.A stale snapshot from the past or future is not partially acceptable; the loss occurs at the first-slot displacement.Source: F. The boundaries: state… · p. 13
  • Frozen evaluation at fifteen shifted operating points lowers PrefDT’s worst-case front quality by 4.3% on average, versus 2.6% for the searched rule, so zero-shot transfer to shifted physics is outside the claim.An in-episode switch of the arrival process does not degrade performance; budget robustness concerns the integral of consumption, not changed environment statistics.Source: F. The boundaries: state… · p. 13

VI. CONCLUSION

  • PrefDT takes the energy–delay trade-off as a run-time input, and one frozen model serves any curve point in one rollout.The energy entry is a running budget decremented by actual fleet spending; a denser front requires more rollouts, not more search.Source: §VI · p. 13
  • Across 26 method variants, PrefDT produces the best trade-off curve of any learned method and holds its energy budget to 0.6% under a mid-flight physics change.The open-loop rule it learned from overruns on every episode; its front reaches 99.7% of a stronger teacher’s front.Source: §VI · p. 13

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