{"id":"2715547c-bee1-4c5d-80ec-b65eb51bfcb6","arxiv_id":"2501.02099","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A receiver buffer of past packets scheduled by a Maximum Gain First policy over age-of-information vectors reduces remote estimation error for a simulated autoregressive source.","lead":"This paper studies a remote estimation system where the receiver keeps a buffer of recent sensor packets and schedules transmissions to minimize estimation error measured by an age-of-information vector. The authors show in a numerical example that a two-packet buffer reduces the optimized average error for an autoregressive source compared with a one-packet buffer.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The b=2 advantage rests entirely on Figure 2's unreported MSE curves; without their derivation or code the scheduling gains and Figure 3 comparison cannot be verified.","rationale":"The reader's weakest assumption points to Figure 2, and I agree that this is the load-bearing input. The entire numerical argument depends on the Kalman-filter MSE as a function of the AoI vector, but the paper does not report how these curves were generated: no state-space realization of the AR(4) process, no measurement model, no noise covariance matrices, no steady-state or finite-horizon specification, and no code. Since the Bellman costs in (12)-(13), the MGF gains in (15), and the final comparison in Figure 3 all consume these curves, an independent reproduction is necessary before the quantitative claims can be accepted. I also note a smaller but related issue: the abstract says 'non-Markovian sources,' but AR(4) is a fourth-order Markov process, so the experiment supports only an order-4 Markov source, not a general non-Markovian one. That said, the qualitative direction of the result is plausible and even information-theoretically expected, because an optimal estimator with access to an additional stored packet cannot have larger MMSE than one without it. Therefore I do not recommend rejection; the paper should be accepted only after the curves are made reproducible or replaced with an analytical derivation. This matches the reader's CONDITIONAL verdict, so no change is needed.","tokens_in":7610,"tokens_out":8526,"duration_ms":94702,"concrete_test":"Reconstruct the AR(4) in state-space form, e.g., state [X_t, X_{t-1}, X_{t-2}, X_{t-3}], measurement at age Δ equal to the appropriate component, and noise variance 1; compute the Kalman error covariance for (Δ1, Δ2) pairs and regenerate Figure 2. Then rerun the MGF algorithm and Figure 3 with the recomputed err(Δ). If the b=2 MSE curve is not pointwise at or below the b=1 curve, or if Figure 3's gap reverses, the central numerical claim fails. Ideally release the script so the curves can be checked exactly.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section V presents the sole evidence for the abstract's claim. The immediate costs errn(Δ) in Bellman equations (12)-(13) are taken from Figure 2, which plots Kalman-filter MSE for the AR(4) source but gives no state-space model, no measurement equation, no noise covariances, and no formula for the MSE given the AoI vector. The paper only states that MSE is 'found to be non-monotonic ... consistent with [21]'. These curves determine the gains α in (15), hence the MGF policy, and the b=1 vs b=2 comparison in Figure 3. If the curves are off by a small amount, or if the Kalman filter was not run to steady state, the MGF gain ordering and the reported buffer advantage could change. In addition, the label 'non-Markovian' is applied to AR(4), which is a fourth-order Markov process; the general claim is supported neither analytically nor by more source models. The qualitative result that extra stored packets cannot increase MMSE is likely true by monotonicity, so I would not reject the conclusion; but the numerical demonstration is not currently reproducible.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a remote estimation system in which N sensors transmit status updates over M shared wireless channels to a receiver equipped with a finite buffer per sensor. The receiver stores the b most recently received packets from each sensor, and the state of each source is an AoI vector describing the ages of the buffered packets. The transmission scheduling problem is formulated as a discounted infinite-horizon RMAB, relaxed via Lagrangian dual decomposition, and solved by a Maximum Gain First (MGF) policy that selects sensors with the largest Q-value differences. A numerical example with an AR(4) source and a Kalman filter at the receiver is used to claim that a buffer of size 2 reduces the average estimation error relative to a buffer of size 1, and the abstract and conclusion state that receiver buffering improves estimation for non-Markovian sources.","tokens_in":7822,"tokens_out":4336,"duration_ms":45397,"significance":"If the result holds, the paper provides a useful extension of AoI-based scheduling from a scalar age to an age vector, and the MGF approach offers a way to avoid the indexability requirement of Whittle-index policies in a restless bandit formulation. The authors are also transparent that the MGF policy is adopted from their prior work [22], [23]. However, the central numerical claim rests on a single AR(4) example whose underlying MSE curves are not specified in the manuscript, and the term \"non-Markovian\" is applied to a source that is in fact fourth-order Markov. The paper would be more convincing if the evaluation included reproducible details, additional source models, and scheduling baselines; the current manuscript does not yet support the strength of the abstract's general claim.","major_comments":[{"comment":"The functions err(Δ1) and err(Δ1,Δ2) are the immediate costs in the Bellman equations (12)-(13), and through (15) they determine the MGF gains and the entire buffer comparison in Figure 3. The manuscript does not give the state-space representation used for the AR(4) model in (18), the measurement equation, the noise covariances, the Kalman filtering equations, the procedure for computing the MSE from the AoI vector, or the number of Monte Carlo runs with error bars. Since these curves are the sole numerical input to the scheduling policy, the central result cannot be reproduced or independently verified from the information provided.","section":"Section V, Figure 2"},{"comment":"The paper's main claim concerns \"non-Markovian sources,\" but the only source in the evaluation is the fourth-order autoregressive process X_{n,t} = 0.1 X_{n,t-1} + 0.8 X_{n,t-4} + W_{n,t}. An AR(4) process is a fourth-order Markov process and can be recast as a first-order Markov process by augmenting the state with lagged values. Thus the term \"non-Markovian\" is misleading, and the general claim is supported neither analytically nor by a broader set of source models. The authors should either qualify the claim or provide evidence for sources that are not finite-order Markov.","section":"Abstract and Section V"},{"comment":"The comparison between buffer sizes b=1 and b=2 uses the proposed MGF policy, but no alternative scheduling policies are evaluated. Without baselines such as a greedy policy, a Whittle-index policy when available, or a simple round-robin scheme, it is unclear whether the observed improvement is due to the buffer memory itself or to the specific scheduling rule. Since the abstract's conclusion is about the benefit of buffering, the experiment should separate the effect of the buffer from the effect of the scheduling policy.","section":"Section V, Figure 3"},{"comment":"The MGF policy is adopted from [22], [23] and is defined as the solution of the Lagrangian-relaxed problem, but the manuscript provides no performance guarantee, optimality gap, or asymptotic optimality argument for the original constrained problem (5)-(6). The policy is therefore heuristic for the considered model, and the absence of any bound weakens the claim that the proposed scheduling is \"optimized\" in the numerical section. A short discussion of the known theoretical status of MGF-type policies would help the reader calibrate the strength of the conclusions.","section":"Section IV-C"}],"minor_comments":[{"comment":"Equation (5) contains a limit superior over T of an infinite sum over t=0 to infinity; with a fixed discount factor γ<1 the limit superior is redundant. This likely reflects an editing error from an average-cost formulation, and it should be clarified.","section":"Equation (5)"},{"comment":"The caption states \"AoI Δ1(t) vs estimation error with fixed Δ2(t)=3,\" but the b=1 case has no second age component. Please specify which curves correspond to b=1 and b=2 and what the fixed age means for the single-packet case.","section":"Figure 2 caption"},{"comment":"The phrase \"the data at the receiver may become outdated\" is colloquial; also \"an estimator whose estimation performance\" is awkward. A brief proofreading pass would improve clarity.","section":"Section I"},{"comment":"The related-work paragraph mentions \"non-indexable scheduling policies\" and then says the MGF policy was also called the Optimal Lagrange Index policy in [27], LP-Index policy in [28], and Gain Index policy in [26]. Adding one sentence explaining the relation among these names and the proposed policy would help readers who are not familiar with this literature.","section":"Section II"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is quite short for the breadth of its claims and relies heavily on the authors' prior work for the scheduling policy. The main concern is not the modeling framework, which is reasonable, but the lack of reproducibility of the numerical section and the overstatement of \"non-Markovian\" support from a single AR(4) example. I would advise the editor that the paper can become acceptable after the numerical details are supplied and the claims are qualified."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe new thing here is the receiver-buffer age-vector formulation for remote estimation scheduling, and the paper is honest that the Maximum Gain First policy is [22],[23] renamed. That is fine: the buffer state model is the contribution, and it is laid out clearly. The RMAB relaxation and MGF adaptation are standard, and the authors flag the indexability issue rather than hand-wave it.\n\nThe soft spots are in the evaluation. The abstract's claim that buffering helps non-Markovian sources rests on Figure 2, which plots Kalman-filter MSE versus the AoI vector for an AR(4) source. The paper gives no state-space model, no measurement equation, no noise covariances, and no formula for how MSE depends on the age vector. Those curves set the gains in (15) and drive the b=1 vs b=2 comparison in Figure 3. Without the derivation or code, the numerical result is not checkable. Also, AR(4) is fourth-order Markov, not non-Markovian, and there is only this one source model, no error bars, and no scheduling baselines. The qualitative conclusion that b=2 cannot be worse than b=1 is essentially monotonicity and likely true; the quantitative gain is not established.\n\nI would not reject the idea. The formulation is reasonable and the missing pieces are fixable: supply the MSE computation, add a second source model, compare with a greedy or Whittle policy, and release code. The paper deserves a serious referee, but the referee should ask for those before acceptance. If you work on AoI-based scheduling, the buffer-vector state space is worth knowing about; just do not cite the measured gain as fact.\n\nRecommendation: send to peer review, but expect major revision on the evaluation side.","headline":"A clear AoI-vector buffer model with honest provenance, but the headline numerical result is not reproducible without the missing MSE derivation.","tokens_in":8316,"tokens_out":2368,"would_cite":true,"duration_ms":23366,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A receiver that stores multiple packets estimates non-Markovian sources more accurately than one that keeps only the freshest packet.","keywords":["age of information","AoI vector","remote estimation","receiver buffer","restless multi-armed bandit","Maximum Gain First","Kalman filter","non-Markovian sources"],"falsifier":"Recompute the Kalman-filter mean-squared error for the AR(4) source with buffer size 2 at specific age pairs, such as Δ1=1 and Δ2=3, and compare with the b=1 curve at the same ages; if the b=2 estimate is not strictly better for the age pairs the scheduler actually visits, the buffer advantage reported in Figure 3 would not hold.","tokens_in":7415,"feed_emoji":"📡","tokens_out":5655,"duration_ms":54102,"temperature":0.7,"pith_summary":"This paper argues that a remote estimator can do better when the receiver keeps a small buffer of recently received packets rather than only the freshest one. For sources whose current value depends on more than the latest observation, the age vector of all buffered packets becomes the state that drives both estimation and scheduling. The authors formulate the scheduling problem as a restless multi-armed bandit, relax it with a Lagrange multiplier, and derive a Maximum Gain First policy that selects sensors by the Q-value gain of transmission. Numerical results for an AR(4) process with a Kalman filter show that a two-packet buffer reduces average estimation error relative to the one-packet baseline.","feed_headline":"Receiver memory lowers estimation error for non-Markovian sources","feed_subtitle":"A two-packet buffer beats the standard one-packet setup for sources with temporal dependence under an AoI-vector scheduler.","key_machinery":"The central object is the age-of-information vector Δ_n(t) = (Δ_{n,1}(t), . . . , Δ_{n,b}(t)) of the b packets stored for sensor n. Together with the buffer contents, it forms the state of a restless multi-armed bandit; the scheduling rule is the Maximum Gain First (MGF) policy, which at each slot transmits to at most M sensors with the largest non-negative gain α_{n,λ*}(Δ) = Q*_{n,λ*}(Δ,0) − Q*_{n,λ*}(Δ,1), the Q-value benefit of sending. Because the gain comes from a Lagrangian-relaxed dual solution rather than a Whittle index, the policy needs no indexability condition. The AoI vector is what lets the scheduler reason about the value of all stored packets, not just the freshest.","core_discovery":"The central claim is that receiver-side memory improves remote estimation for non-Markovian sources, and that the improvement can be captured by an age-of-information vector rather than by tracking full packet contents. The paper constructs a scheduling policy, Maximum Gain First, based on the Q-value difference α_{n,λ*}(Δ) = Q*_{n,λ*}(Δ,0) − Q*_{n,λ*}(Δ,1), computed from a Lagrangian relaxation of the restless multi-armed bandit, and shows numerically that with buffer size 2 the optimized average mean-squared error is lower than with buffer size 1 for an AR(4) source under erasure channels. This extends the conventional b=1 AoI framework, suited to Markovian sources, to sources with longer temporal dependence. The authors also note that this appears to be the first AoI-vector-based scheduling formulation with a receiver-side buffer.","pith_inferences":["If the effect is robust, the optimal buffer size may scale with the source's memory order and the channel's packet-loss probability; a source with longer temporal dependence could benefit from b>2, while an i.i.d. source would gain nothing from any buffer.","The MGF policy's independence from indexability suggests it may extend to multiple channels and nonlinear estimators beyond Kalman filtering, though the paper only simulates one channel and two sensors.","Because the MSE is non-monotonic in the AoI vector, the scheduler implicitly trades freshness against informativeness: transmitting a fresh packet may be less valuable than transmitting a packet that fills a gap in the buffer's history.","The buffer's benefit can be viewed as a form of implicit prediction: stored packets act as a finite memory that lets the estimator exploit autocorrelation without changing the underlying transmission protocol."],"forward_implications":["For non-Markovian sources, receiver memory is structurally useful: with buffer size 2, the optimized average estimation error falls below the b=1 baseline across the simulated transmission probabilities.","The AoI vector is a sufficient state for scheduling: the scheduler needs only the ages of the stored packets, not their values, to make transmission decisions.","The Maximum Gain First policy applies to restless multi-armed bandits where Whittle indexability is hard to verify, because it only requires solving relaxed per-arm MDPs and computing Q-value differences.","The estimation error as a function of the AoI vector can be non-monotonic, so a fresher packet does not always help more than an older packet that completes the information available in the buffer.","For a two-sensor, one-channel system with an AR(4) source, the two-packet buffer improves the optimized average estimation error compared with the standard one-packet setup."],"supporting_citations":[{"why":"Supplies the non-monotonic estimation-error-vs-AoI relation and remote-inference formulation on which the paper's errn(Δ) is based.","marker":"[21]"},{"why":"Introduces the Net-gain Maximization policy, renamed Maximum Gain First here, and the Q-value gain definition used for scheduling.","marker":"[22]"},{"why":"Provides another instance of the same gain-based policy for context-aware status updating, supporting the claim that it avoids the indexability condition.","marker":"[23]"},{"why":"Sets up the restless multi-armed bandit and Lagrangian relaxation framework that the paper adapts, and the Whittle index approach it deliberately bypasses.","marker":"[24]"},{"why":"Establishes the conventional b=1 remote-estimation model for a Markovian Wiener process, the baseline the buffer extension generalizes.","marker":"[1]"},{"why":"Provides a Whittle-index scheduling policy for multiple Gauss-Markov processes, the type of Markovian baseline against which the buffer-based approach is positioned.","marker":"[5]"}],"fun_headline_variants":["Receiver memory slashes estimation error for non-Markovian sources","Two-packet receiver buffer beats one for non-Markovian sources","AoI-vector scheduler with receiver memory lowers error","Buffer at receiver: lower error for non-Markovian sources","Receiver buffer improves estimation for temporally dependent sources"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire buffer advantage rests on the numerically generated curves in Figure 2 that relate the AoI vector to Kalman-filter mean-squared error; if those curves are inaccurate or the age-vector state reduction is invalid, the simulated performance gap in Figure 3 collapses.","fun_headline_variants_meta":{"raw":{"variants":["Receiver memory slashes estimation error for non-Markovian sources","Two-packet receiver buffer beats one for non-Markovian sources","AoI-vector scheduler with receiver memory lowers error","Buffer at receiver: lower error for non-Markovian sources","Receiver buffer improves estimation for temporally dependent sources"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000804,"raw_usage":{"total_tokens":3473,"prompt_tokens":824,"completion_tokens":2649,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":440,"completion_tokens_details":{"reasoning_tokens":2564}},"tokens_in":440,"tokens_out":2649,"duration_ms":18944,"temperature":1.0,"reasoning_tokens":2564,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:14:38.346741+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute the Kalman-filter mean-squared error for the AR(4) source with buffer size 2 at specific age pairs, such as Δ1=1 and Δ2=3, and compare with the b=1 curve at the same ages; if the b=2 estimate is not strictly better for the age pairs the scheduler actually visits, the buffer advantage reported in Figure 3 would not hold.","supporting_citations":[{"cited_title":"Timely commu- nications for remote inference,","cited_arxiv_id":null,"evidence_quote":"Supplies the non-monotonic estimation-error-vs-AoI relation and remote-inference formulation on which the paper's errn(Δ) is based."},{"cited_title":"Context- aware status updating: Wireless scheduling for maximizing situational awareness in safety-critical systems,","cited_arxiv_id":null,"evidence_quote":"Provides another instance of the same gain-based policy for context-aware status updating, supporting the claim that it avoids the indexability condition."},{"cited_title":"Restless bandits: Activity allocation in a changing world,","cited_arxiv_id":null,"evidence_quote":"Sets up the restless multi-armed bandit and Lagrangian relaxation framework that the paper adapts, and the Whittle index approach it deliberately bypasses."},{"cited_title":"Remote estimation of the wiener process over a channel with random delay,","cited_arxiv_id":null,"evidence_quote":"Establishes the conventional b=1 remote-estimation model for a Markovian Wiener process, the baseline the buffer extension generalizes."},{"cited_title":"A Whittle index policy for the remote estimation of multiple continuous Gauss-Markov processes over parallel channels,","cited_arxiv_id":null,"evidence_quote":"Provides a Whittle-index scheduling policy for multiple Gauss-Markov processes, the type of Markovian baseline against which the buffer-based approach is positioned."}],"review_version":1}