A Dynamic Improvement Framework for Vehicular Task Offloading

Bojie Lv; Qianren Li; Rui Wang; Yuncong Hong

REVIEW 4 major objections 6 minor 11 references

A Dynamic Improvement Framework for Vehicular Task Offloading

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read A low-complexity online scheduler provably never exceeds the average cost of its deterministic preplan for vehicular task offloading.

desk verdict Useful low-complexity scheduler idea, but the advertised upper bound is unsupported: the acceptance test only controls an approximate value function that is never shown to bound true cost. read the letter →

arxiv 2501.11333 v1 pith:TOVALBYN submitted 2025-01-20 eess.SY cs.NIcs.SY

Qianren Li , Yuncong Hong , Bojie Lv , Rui Wang This is my paper · ORCID

classification eess.SYcs.NIcs.SY MSC 90C4090C39

keywords vehicularedgecomputingtaskoffloadingMarkovdecisionprocessapproximatevaluefunctionreferenceschedulingdynamicimprovementaveragecostboundtrafficsimulator

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper addresses task offloading from vehicles with random speeds to an edge server through base stations, where the exact trajectory is unknown ahead of time. It formulates cell association, uplink time, and throughput allocation as a finite-horizon Markov decision process, whose optimal policy normally requires expensive value iteration. The proposed dynamic improvement framework first solves a deterministic problem on the vehicles' average trajectories to produce a reference schedule, then uses that schedule to build an approximate cost-to-go function and refines the action slot by slot. The paper's central claim is that the resulting online policy has average total cost no larger than the reference schedule at every step, so the approximation never sacrifices the pre-planned guarantee. That is significant because the online optimizer is low-complexity while still carrying a provable performance bound.

What carries the argument

The load-bearing object is the approximate value function $\tilde V_{t+1}(S_{t+1}) = \sum_{n\in\mathcal N} \tilde V_{n,t+1}(d_{n,t+1}, l_{n,t+1})$, where each vehicle term combines the non-empty-buffer indicator cost $f^1_{n,t+1}$ and the energy cost $f^2_{n,t+1}$ defined in Table I. This function replaces the true Bellman value function in the per-slot problem P6, making the optimization tractable while encoding what the reference schedule can still achieve from the current state. The acceptance inequality then decides between the newly optimized action and the reference action, and the reference schedule's remaining throughput allocation is updated by the clipping rule in equation (19). The stated performance guarantee of Lemma 2 rests on this cycle of approximation, acceptance, and update.

What would settle it

Construct a small instance with, say, one vehicle, one or two base stations, and $T=2$, where the reference schedule is deliberately optimistic about the last slot's channel. In slot 1, a candidate action that passes the acceptance inequality $c_t(S_t,A^*_t)+\sum_{S_{t+1}}P[S_{t+1}|S_t,A^*_t]\tilde V_{t+1}(S_{t+1}) \le c_t(S_t,A^{(t-1)}_t)+\sum_{S_{t+1}}P[S_{t+1}|S_t,A^{(t-1)}_t]\tilde V_{t+1}(S_{t+1})$ can be found, yet exhaustive enumeration of both slots shows its true remaining cost exceeds the reference schedule's true remaining cost. If such an instance exists, Lemma 2's inequality fails.

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Extended reading notes

Core claim

The central claim is Lemma 2: for the dynamic improvement framework composed of reference scheduling initialization, per-slot online optimization, and reference throughput update, the inequality $C_t(S_t,\tilde\Omega) \le C_t(S_t,\Omega_{t-1}^H)$ holds for every $t \in \{1,2,\ldots,T-1\}$. In words, from any slot onward the expected remaining cost of the online scheduler is no larger than the expected remaining cost of the deterministic reference schedule. The mechanism is the acceptance test in Section IV-B: the optimized action is applied only when its current cost plus the approximate value function $\tilde V_{t+1}$ is no larger than the same expression for the reference action, and otherwise the reference action is kept. The paper also constructs the approximate value function explicitly through Table I, using an achievable future cost for each vehicle based on residual buffered bits and current position. The proof of Lemma 2 is given as immediate from this stepwise suppression of cost.

Load-bearing premise

The proof assumes that the approximate value function $\tilde V_{t+1}$ built from the reference schedule is an accurate upper bound or faithful surrogate for the true future cost under a candidate action, so that a candidate passing the acceptance test truly lowers the average cost; this property is not established in the paper.

Editorial extensions

If this is right

The online policy never exceeds the reference schedule's average remaining cost, so the pre-planned deterministic schedule acts as a safety net at every slot.
Per-slot optimization decouples by vehicle once throughput is fixed, so the method avoids value iteration's exponential growth in the number of vehicles.
The same per-scheduling-period design can be repeated on a rolling horizon, with tasks not fully offloaded in one period treated as new tasks in the next.
In the CARLA-based simulation with 5 vehicles and 3 base stations, the framework reports 54.83% lower average cost than pre-allocation-only, 72.84% lower than maximum power, and 43.36% lower than no pre-allocation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The guarantee is relative to the reference schedule, not to the true optimal MDP policy; the paper gives no bound on the gap to optimality, so the surrogate's tightness is an open question.
The same deterministic-first approximation could be applied to other stochastic scheduling problems, as long as an achievable future-cost expression like Table I can be derived for the reference policy.
A high rejection rate of candidate actions under the acceptance test would be a practical indicator that the approximate value function is too optimistic, suggesting the reference schedule should be re-derived.
Comparing the realized costs against exact value iteration on small instances would directly reveal how much performance is lost by replacing the true value function with the reference-based surrogate.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Punchline: the central guarantee in Lemma 2 does not follow from the material in the paper. The acceptance test compares actions by c_t + E[eV_{t+1}]; for this to imply true cost non-increase, eV must upper-bound the true continuation cost under the future policy eΩ, and the same eV must remain valid after the Section IV-C update. Neither is established. Lemma 1 only gives the cost of one feasible adjustment of the reference schedule, not a bound on eΩ. The proof of Lemma 2 is one sentence (“straightforward…”), and that sentence is exactly where an induction would need to appear. The stress-test note is correct on this.

What is genuinely new: using a deterministic pre-schedule to build an analytical approximate value function and then improving online, with reference update, is a nice application-level variant of rollout and approximate dynamic programming. It is not in the cited vehicular offloading papers, and it plausibly avoids value iteration. The model is clearly stated, the convex subproblems are handled sensibly, and the piecewise convexity in P8 is acknowledged. Credit also for using CARLA and 500 trials.

Soft spots, in proportion. The missing Lemma 2 proof is load-bearing because the abstract and conclusion sell the “non-trivial upper bound.” The alternating minimization in Section IV-B has no convergence proof, though that is less central. The simulations lack error bars and use only three baselines; the gains are large, so this is a minor issue, but confidence intervals and a rollout-style baseline would strengthen the empirical claim.

Overall, the framework may well work as a heuristic, and the empirical evidence is suggestive. But as written, the theoretical guarantee is unsupported. A revised version that either proves the bound under a correct induction or clearly downgrades it to a heuristic claim could be salvageable. The paper deserves a serious referee—the idea is solid enough to warrant one careful revision cycle, and the flaw is the kind a competent referee can check. I would not desk-reject it. I would not cite the bound as proven, and I would not bring it to reading group unless the group is specifically about approximate DP in edge computing.

Referee Report

4 major / 6 minor

Summary. The manuscript formulates vehicular task offloading with random velocities as a finite-horizon MDP, in which the joint BS association, uplink time, and throughput allocation are optimized. To avoid the computational cost of value iteration, the authors propose a two-phase framework: an offline deterministic pre-allocation builds a reference schedule from average trajectories, and an online phase uses a reference-based approximate value function \tilde{V} in a one-step lookahead, with the reference schedule updated after each slot. The central theoretical claim is Lemma 2, Eq. (20): the expected total cost of the proposed dynamic policy is upper-bounded by that of the reference schedule at every time. Simulations with the CARLA traffic simulator report average cost reductions of 43.36%, 54.83%, and 72.84% against three baselines.

Significance. If the claimed upper bound were rigorously established, the paper would provide a low-complexity alternative to value iteration for vehicular task offloading, with an analytical performance guarantee relative to a deterministic pre-schedule. The system model is explicit, the per-vehicle throughput subproblems in Section IV-A are clearly derived, and the use of a high-fidelity traffic simulator is a strength. However, the central theoretical guarantee is currently supported only by a one-sentence proof, the convergence of the alternating minimization is not addressed, and the numerical evaluation lacks confidence intervals and strong baselines. The significance of the paper is therefore conditional on a substantive revision of the proof and the empirical reporting.

major comments (4)

[Section IV-B, Lemma 2 (Eq. 20)] The proof of Lemma 2 is a single sentence and does not establish the claimed upper bound. The acceptance test compares candidate and reference actions using the approximate value function \tilde{V}_{t+1} from Lemma 1, but Lemma 1 only shows that \tilde{V}_{t+1} is the cost achievable by one particular policy that adjusts the reference schedule; it is not shown to be an upper bound on the true future cost of the proposed policy \tilde{\Omega}. Moreover, after the t-th slot the reference schedule is updated in Section IV-C, so the \tilde{V} used at t+1 is rebuilt from \Omega_t^H and differs from the \tilde{V} used in the t-th acceptance test; no monotonicity of \tilde{V} under the update in Eq. (19) is proved. Consequently, an action can pass the acceptance test while increasing the true expected total cost, and the inequality C_t(S_t, \tilde{\Omega}) \le C_t(S_t, \Omega_{t-1}^H) does not follow from the stated arguments. The proof must be replaced by a rigorous induction that relates the \tilde{V} appearing in the acceptance test to the true continuation cost of \tilde{\Omega} and explicitly accounts for the reference-schedule update.
[Section IV-B, after P8] The alternating minimization of P7 and P8 is stated to be applied "iteratively until convergence," but no convergence proof is given. Since P6 is non-convex for t<T, the iterates may converge to a point that is not a local minimum, or may not converge at all. Because the acceptance test relies on the quality of the candidate action A_t^*, the absence of a convergence or termination guarantee undermines the algorithm description. Please provide a convergence proof, a fixed iteration count with a suboptimality bound, or a clear statement of the heuristic nature of the alternating minimization.
[Section IV-B, statement on P6] The claim that "P6 is convex when t = T" is incorrect as written. The action at time T includes the binary association matrix E_T through constraint C1, so the terminal problem is a mixed-integer program and is not convex. This is not a mere presentation issue, because the terminal action is part of the overall policy whose cost is bounded in Lemma 2. The authors should either solve the terminal association exactly by enumeration over the M^N possible associations, or add a relaxation-and-rounding step with an explicit performance statement.
[Section V] The simulation study reports average total costs and CDFs obtained from 500 trials, but no confidence intervals, standard deviations, or statistical tests are provided; the reported gains of 54.83%, 72.84%, and 43.36% are therefore not established with statistical significance. In addition, the baselines are all either special cases of the proposed framework or simple heuristic schemes; there is no comparison with optimal value iteration, which is the reference solution that the paper claims to replace. Please add error bars or confidence bands, and compare against a value-iteration-based scheduler on a small instance where the optimal solution is computable.

minor comments (6)

[Section IV-A] The notation \bar{r}_{n,t} is used both as a function of \tau_{n,t}^{(0)} and as the resulting value in Eq. (14); please use distinct notation for the function and the value.
[Lemma 1 and Eq. (18)] Lemma 1 uses the quantities r_{n,t+k}^s before they are defined in Eq. (18); the definition of r^s should be moved before Lemma 1 or a forward reference should be added.
[Table I] The piecewise expressions in Table I are difficult to parse, especially the third row, where the expression for f_{n,t+1}^1 contains mismatched parentheses; please re-derive and polish all cases.
[Section V, baselines] The baseline "No Pre-Allocation" is not clearly distinguished from "Maximum Power," because both use the maximum-power association rule; please state explicitly which quantities are optimized in each baseline.
[Reference [10]] Reference [10] lists the venue as "CoLR," but the correct acronym for the Conference on Robot Learning is CoRL; please also supply the conference location and page range.
[Section I and IV] The paper repeatedly claims that the proposed framework is low-complexity, but it never quantifies the complexity of value iteration or of the alternating minimization; an explicit complexity comparison would strengthen the contribution.

Circularity Check

0 steps flagged · score 0.0 of 10

No load-bearing circularity: the central derivation does not reduce to its inputs; Lemma 2 has a proof gap, but that is an omitted argument, not a circular reduction.

full rationale

The paper's derivation chain is not circular. The reference schedule is obtained by deterministic optimization (P2–P5) and then used to construct the approximate value function eV in Lemma 1; the acceptance test in Section IV-B compares actions through c_t + E[eV], which is a different quantity from the true average cost C_t defined in (10). Lemma 2's one-sentence proof (“The conclusion is straightforward since the average system cost of the reference scheduling is suppressed by the online optimization of Section IV-B in each time slot”) is under-supported: it would require an additional domination argument showing that the online policy's true future cost remains below eV and that eV lies below the reference cost. That is an omitted proof step, but it is not a circular reduction: no equation identifies eV with C_t, the theorem is not used as an input to the algorithm, and the reference update in (19) is not defined in terms of the claimed bound. The only author-overlapping citation is [8], used to generate transition probabilities in the simulator; it is not load-bearing for the theoretical claims. The numerical comparisons against Pre-Allocation Only, Maximum Power, and No Pre-Allocation are external benchmarks, not outputs of the acceptance rule. Therefore no circular step is established and the circularity score is 0.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

No new physical entities are introduced. The only hand-chosen numbers are the two cost weights. The framework assumes known trajectory transition probabilities and relies on ergodic-capacity and high-SNR approximations. The main hidden assumption is that eV is a faithful surrogate for true cost, which is also the weakest step in the proof of the central bound.

free parameters (2)

ω1 (energy weight) = 2
Hand-chosen weight in the per-slot cost function; affects the trade-off between buffer penalty and energy but the framework works for any positive value.
ω2 (unfinished-task penalty) = 5
Hand-chosen terminal penalty in the last time slot; selected in the simulation setup of Section V.

assumptions (4)

domain assumption Vehicle locations follow a stationary Markov chain with known transition matrices P_n (Section II-A).
The MDP formulation and the approximate value functions require P_n as input; if P_n is inaccurate, the scheduler has no mechanism to adapt.
domain assumption Time slot duration is large enough for ergodic channel capacity (Section II-B).
The throughput expression in (6) ignores block-fading details; this is a common idealization but affects the calculated costs.
domain assumption High-SNR approximation is valid for the reference throughput planning (Section IV-A, problems P4 and P5).
The energy-to-throughput conversion uses log2(x) instead of log2(1+x); at low SNR the derived costs become inaccurate.
ad hoc to paper Lower approximate value function eV implies lower true average cost (Lemma 2 proof).
This hidden premise is what makes the claimed upper bound work; no proof is given, and it is unlikely to hold without eV being a tight upper bound on true future cost.

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Cite this review

Pith. "Pith review of A Dynamic Improvement Framework for Vehicular Task Offloading." pith.science (2026). https://pith.science/paper/TOVALBYN

@misc{pith2026250111333,
  author       = {Pith},
  title        = {Pith review of: A Dynamic Improvement Framework for Vehicular Task Offloading},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TOVALBYN}},
  note         = {Machine review of arXiv:2501.11333}
}

read the original abstract

In this paper, the task offloading from vehicles with random velocities is optimized via a novel dynamic improvement framework. Particularly, in a vehicular network with multiple vehicles and base stations (BSs), computing tasks of vehicles are offloaded via BSs to an edge server. Due to the random velocities, the exact trajectories of vehicles cannot be predicted in advance. Hence, instead of deterministic optimization, the cell association, uplink time and throughput allocation of multiple vehicles in a period of task offloading are formulated as a finite-horizon Markov decision process. In the proposed solution framework, we first obtain a reference scheduling scheme of cell association, uplink time and throughput allocation via deterministic optimization at the very beginning. The reference scheduling scheme is then used to approximate the value functions of the Bellman's equations, and the actual scheduling action is determined in each time slot according to the current system state and approximate value functions. Thus, the intensive computation for value iteration in the conventional solution is eliminated. Moreover, a non-trivial average cost upper bound is provided for the proposed solution framework. In the simulation, the random trajectories of vehicles are generated from a high-fidelity traffic simulator. It is shown that the performance gain of the proposed scheduling framework over the baselines is significant.

Figures

Figures reproduced from arXiv: 2501.11333 by the authors.

**Figure 2.** The CDFs of total cost. Proposed No Pre-Allocation Pre-Allocation Only Maximum Power 50 100 150 200 250 300 350 400 Average Total Cost 104.53 184.55 231.44 384.87 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗

**Figure 3.** The comparison of average total costs. V. PERFORMANCE EVALUATION In this section, we evaluate the performance of the proposed solution framework. The vehicle’s trajectories are randomly generated from the CARLA simulator [10] in the road map Town01. As shown in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

[1] [1]

11em plus .33em minus .07em 4000 4000 100 4000 4000 500 `\.=1000 = #1 \@IEEEnotcompsoconly \@IEEEcompsoconly #1 * [1] 0pt [0pt][0pt] #1 * [1] 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEcompsocnotconfonly \@IEEEauthorblockAstyle \@IEEEcompsocnotconfonly \@IEEEcompsocconfonly \@IEEEauthordefaulttextstyle \@IEEEcompsocnotconfonly \@IEEEauthor...

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Zhang, Y

L. Zhang, Y. Sun, Y. Tang, H. Zeng, and Y. Ruan, ``Joint Offloading Decision and Resource Allocation in MEC-enabled Vehicular Networks ,'' in Proc. IEEE Vehicular Technology Conference ( VTC2021-Spring ) , Apr. 2021, pp. 1--5

work page 2021

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Z. Jia, Z. Zhou, X. Wang, and S. Mumtaz, ``Learning- Based Queuing Delay-Aware Task Offloading in Collaborative Vehicular Networks ,'' in Proc. IEEE Int. Conf. Commun. (ICC), Jun. 2021, pp. 1--6

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H. Cho, Y. Cui, and J. Lee, ``Energy- Efficient Cooperative Offloading for Edge Computing-Enabled Vehicular Networks ,'' IEEE Trans. Wireless Commun., vol. 21, no. 12, pp. 10\,709--10\,723, Dec. 2022

work page 2022

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Maleki, M

H. Maleki, M. Ba s aran, and L. Durak-Ata , ``Handover- Enabled Dynamic Computation Offloading for Vehicular Edge Computing Networks ,'' IEEE Trans. on Vehicular Technology, vol. 72, no. 7, pp. 9394--9405, Jul. 2023

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X. Zhang, J. Zhang, Z. Liu, Q. Cui, X. Tao, and S. Wang, `` MDP-Based Task Offloading for Vehicular Edge Computing Under Certain and Uncertain Transition Probabilities ,'' IEEE Trans. on Vehicular Technology, vol. 69, no. 3, pp. 3296--3309, Mar. 2020

work page 2020

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Y. Liu, H. Yu, S. Xie, and Y. Zhang, ``Deep Reinforcement Learning for Offloading and Resource Allocation in Vehicle Edge Computing and Networks ,'' IEEE Trans. on Vehicular Technology, vol. 68, no. 11, pp. 11\,158--11\,168, Nov. 2019

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