{"id":"05821889-28d6-4346-bad5-812c9eaf1d6d","arxiv_id":"2501.11333","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"high","formal_verification":"none","parameter_count":2,"one_line_summary":"A dynamic improvement framework for vehicular task offloading computes a deterministic reference schedule and then refines each slot's actions via approximate value functions.","lead":"This paper proposes a two-phase scheduler for vehicular task offloading: first compute a deterministic pre-schedule, then refine each time slot using an approximate value function. It claims this dynamic improvement is low-complexity and guaranteed not to do worse than the pre-schedule, which is why edge-computing researchers might care.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Lemma 2's upper bound is unsupported: the acceptance test uses an approximate value function that is never shown to upper-bound the true cost of the continuation policy, and the §IV-C update changes that value function after the test.","rationale":"The paper's empirical evaluation may be valid, but the advertised theoretical guarantee is the non-trivial average-cost upper bound in Lemma 2. The proof of that lemma is a single sentence and does not bridge the gap between the approximate value function used in the acceptance test and the true cost of the policy that is actually executed. The reader's weakest-assumption analysis identifies this same gap: the acceptance test compares c_t + E[eV_{t+1}], but eV_{t+1} is only an achievable cost of an adjusted reference continuation, not a bound on the true continuation cost of eΩ. My reading adds a second, more specific difficulty: the reference schedule is updated after each slot, so the eV used at slot t+1 is recomputed from the updated schedule and is not the same object that appeared in the slot-t acceptance inequality. A careful induction would need to show C_{t+1}(S_{t+1}, eΩ) ≤ eV^{(t-1)}_{t+1}(S_{t+1}) using the pre-update value, or prove a monotonicity property of eV under Eq. (19). Neither is present. Because the central theoretical claim is unsupported, the reader's REJECT verdict is appropriate; if the authors supply the missing induction or weaken the claim to a heuristic with empirical gains, a CONDITIONAL acceptance could be reconsidered. The proposed brute-force check on a small MDP would settle whether the missing inequality actually holds or admits counterexamples.","tokens_in":10365,"tokens_out":8688,"duration_ms":95289,"concrete_test":"Implement the algorithm exactly for a minimal instance (N=1 vehicle, M=1 BS, T=3 slots) with the model of §II, using a two-state Markov chain for the vehicle location. Enumerate a fine grid of transition probabilities and weights (ω1, ω2), and for each configuration compute the reference schedule, execute the online improvement of §IV-B/IV-C, and compare the true expected cost C_1(S_1, eΩ) with C_1(S_1, Ω^H_0) by dynamic programming over the small state space. If any grid point violates Eq. (20), Lemma 2 is false. If no violation appears, repeat with T=4 and with N=2 vehicles to stress the induction that the proof omits.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is Lemma 2, Eq. (20): C_t(S_t, eΩ) ≤ C_t(S_t, Ω^H_{t-1}) for all t. The only mechanism offered is the acceptance test in §IV-B, which compares candidate and reference actions by c_t + E[eV_{t+1}]. For this test to suppress true total cost, eV_{t+1} must be an upper bound on the true future cost of the proposed continuation policy eΩ from slot t+1 onward, i.e., C_{t+1}(S_{t+1}, eΩ) ≤ eV_{t+1}(S_{t+1}), and the bound must use the same eV that appears in the acceptance inequality. The paper never establishes this. Lemma 1 only asserts that eV_{t+1} is achievable by adjusting the reference schedule; that makes it the cost of one feasible policy, not an upper bound on the cost of eΩ, which is free to take different actions in later slots. Furthermore, after slot t the reference schedule is updated in §IV-C, so the eV used at t+1 is rebuilt from Ω^H_t and differs from the eV used in the t-th acceptance test. No monotonicity of eV under the update (19) is proved. Consequently, an action can pass the acceptance test while increasing the true expected total cost. The one-sentence proof of Lemma 2 ('straightforward since the average system cost of the reference scheduling is suppressed') is exactly where the missing induction would have to appear; without that induction the claimed non-trivial upper bound does not follow.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","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.","tokens_in":10701,"tokens_out":10547,"duration_ms":113086,"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":[{"comment":"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":"Section IV-B, Lemma 2 (Eq. 20)"},{"comment":"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":"Section IV-B, after P8"},{"comment":"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":"Section IV-B, statement on P6"},{"comment":"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.","section":"Section V"}],"minor_comments":[{"comment":"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.","section":"Section IV-A"},{"comment":"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.","section":"Lemma 1 and Eq. (18)"},{"comment":"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":"Table I"},{"comment":"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.","section":"Section V, baselines"},{"comment":"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":"Reference [10]"},{"comment":"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.","section":"Section I and IV"}],"recommendation":"major_revision","confidential_remarks":"The central criticism in the reader's report lands: Lemma 2 is not proven, and the missing induction is load-bearing. I am recommending major revision rather than rejection because a correct induction may be possible if the update in Eq. (19) makes the approximate value function monotonically non-increasing and if the approximate value function can be shown to dominate the true continuation cost of the proposed policy. However, if the authors cannot provide such a proof, the upper-bound claim should be removed from the abstract and the paper repositioned as a heuristic algorithm; in that case the paper would likely fall below the bar for this venue. The false convexity claim for the terminal problem and the lack of statistical reporting should be fixed regardless."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","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.\n\nWhat 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.\n\nSoft 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.\n\nOverall, 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.","headline":"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.","tokens_in":11200,"tokens_out":2229,"would_cite":false,"duration_ms":24610,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["90C40","90C39"],"pacs":[],"model":"deepseek-v4-flash","headline":"A low-complexity online scheduler provably never exceeds the average cost of its deterministic preplan for vehicular task offloading.","keywords":["vehicular edge computing","task offloading","Markov decision process","approximate value function","reference scheduling","dynamic improvement","average cost bound","traffic simulator"],"falsifier":"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.","tokens_in":10170,"feed_emoji":"🚗","tokens_out":6025,"duration_ms":51798,"temperature":0.7,"pith_summary":"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.","feed_headline":"Vehicle offloading gets a schedule never worse than the pre-plan","feed_subtitle":"A cheap approximate value function upgrades a deterministic schedule slot by slot, with a proven average-cost bound.","key_machinery":"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.","core_discovery":"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.","pith_inferences":["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."],"forward_implications":["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."],"supporting_citations":[{"why":"Provides the high-fidelity traffic simulation method used to obtain transition probability matrices for vehicle trajectories.","marker":"[8]"},{"why":"Supplies the Bellman equation and dynamic programming formulation that the approximate value functions are designed to replace.","marker":"[9]"},{"why":"The CARLA simulator generates the random vehicle trajectories used in the performance evaluation.","marker":"[10]"}],"fun_headline_variants":["Dynamic offloading never worse than pre-planned schedule","Online offloading beats static reference, with proof","Vehicular offloading: dynamic scheduling with cost bound","Dynamic improvement for offloading: never worse than pre-plan","Fast offloading scheduler with cost guarantee"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"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.","fun_headline_variants_meta":{"raw":{"variants":["Dynamic offloading never worse than pre-planned schedule","Online offloading beats static reference, with proof","Vehicular offloading: dynamic scheduling with cost bound","Dynamic improvement for offloading: never worse than pre-plan","Fast offloading scheduler with cost guarantee"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000872,"raw_usage":{"total_tokens":3784,"prompt_tokens":966,"completion_tokens":2818,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":582,"completion_tokens_details":{"reasoning_tokens":2744}},"tokens_in":582,"tokens_out":2818,"duration_ms":23262,"temperature":1.0,"reasoning_tokens":2744,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T18:23:01.763756+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"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.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the high-fidelity traffic simulation method used to obtain transition probability matrices for vehicle trajectories."},{"cited_title":"Zhang, S","cited_arxiv_id":null,"evidence_quote":"Supplies the Bellman equation and dynamic programming formulation that the approximate value functions are designed to replace."},{"cited_title":"Bertsekas, Dynamic Programming and Optimal Control, 4th ed","cited_arxiv_id":null,"evidence_quote":"The CARLA simulator generates the random vehicle trajectories used in the performance evaluation."}],"review_version":1}