Sense Once, Serve Many: Common-Trace Factorized Constrained PPO for Online Sensing-Session Consolidation in Multi-Tenant ISAC Networks

Dang-Dung Vu

cs.NIAug 29, 2026

Sense Once, Serve Many: Common-Trace Factorized Constrained PPO for Online Sensing-Session Consolidation in Multi-Tenant ISAC Networks

Authors: Dang-Dung Vu

Organizations: Faculty of Information Technology, VNU University of Engineering and Technology (VNU-UET), Hanoi 100000, Vietnam

Abstract

Integrated sensing and communication (ISAC) networks can serve compatible requests through shared sensing sessions, but consolidation couples admission, reuse, profile selection, sensing service-level agreements (SLAs), communication quality of service (QoS), and future commitments. We formulate this problem as a constrained Markov decision process and propose Common-Trace Factorized Constrained Proximal Policy Optimization (CT-PPO). During training, stochastic policy replicas share the same primitive workload trace; leave-one-out discounted Monte Carlo return contrasts provide reward credit to applicable actor factors, while constraint credit remains factor/prefix-specific. Across five training seeds and matched workloads, CT-PPO achieves the highest mean macro return, exceeding matched Joint-Credit PPO (JC-PPO) by 0.934 (95% confidence interval [0.702, 1.164]) and SLA-Aware Greedy by 1.847; versus JC-PPO, it reduces sensing-resource cost by 6.277 and raises accepted requests per created session by 0.0806. A four-way ablation shows that the factorized surrogate alone yields no detectable macro-return gain, whereas adding common-trace reward credit produces the dominant improvement. Without retraining, CT-PPO retains a return advantage at low, nominal, and high arrival loads, with the strongest gain under clustered arrivals. Deployment uses public observations and hard masks; CT-PPO's extra parameters are training-side, its actor footprint matches JC-PPO, and actor-only CPU latency is effectively unchanged.

Figures & tables

Fig. 1: Multi-tenant ISAC system and online sensing-session consolidation. At most one focal request is processed per slot. A feasible request may merge into an active sensing session or create a new one; one scheduled session update produces a shared sensing result that is evaluated against each member’s own service requirements. Sensing bandwidth and power reduce the residual resources available to communication users.

Fig. 2: CT-PPO architecture and training-time credit flow. The Set encoder and hard masks feed the factorized actor; leave-one-out common-trace reward credit

A^{\mathrm{CT}}

and factor-specific constraint credit

A_{f}^{C}

drive the constrained PPO update. Replication is used only during training. Schematic labels suppress indices:

(M,G_{m}^{R},\bar{G}_{-m}^{R},A_{f}^{C})

correspond to

(M_{g},G_{g,m}^{R},B_{g}^{R,-m},A_{n,f}^{C_{q}})

below.

Category	Setting
System	$T=200$ slots, $\Delta t=0.1$ s; $L=4$ sensing tenants, $K=6$ communication users, $8$ targets; $B^{\mathrm{tot}}=20$ MHz, $P^{\mathrm{tot}}=40$ W; carrier $6$ GHz.
Geometry/mobility	$[-200,200]^{2}$ m 2 region; initial target/user ranges $30$ – $140$ / $20$ – $180$ m; initial target/user speeds $0$ – $12$ / $0$ – $8$ m/s and acceleration std. $1/0.5$ m/s 2 ; AOI radius $U[15,30]$ m with center-offset std. $4$ m, truncated at half the AOI radius.
Requests	DET/LOC/TRK probabilities $0.35/0.35/0.30$ ; durations $H_{\mathrm{DET}}/H_{\mathrm{LOC}}/H_{\mathrm{TRK}}=3/4/8$ slots; completion values $U[0.8,1.2]/U[1.5,2.5]/U[2.5,4.0]$ ; latest-start slack discrete-uniform on $\{2,\ldots,8\}$ ; update periods DET/LOC on $\{1,2,3\}$ with probabilities $(.25,.45,.30)/(.30,.45,.25)$ and TRK on $\{1,2\}$ with $(.65,.35)$ ; sharing permission $0.9$ ; defer cooldown $\tau_{\mathrm{defer}}=1$ slot.
Physical/quality	$N_{0}=-174$ dBm/Hz; communication/sensing noise figures $7/7$ dB; communication gap $1.5$ dB; sensing front-end gain/system loss $24/3$ dB, effective aperture $0.5$ m; $P_{\mathrm{FA}}=10^{-4}$ , detection gate $0.9$ ; DET/PEB/PCRB thresholds $U[0.85,0.98]$ / $U[1.5,6]$ / $U[1.5,5]$ m; tracking prior covariance diagonal $(25,25,4,4)$ .
Channel processes	Communication path-loss exponent $3$ , shadowing std./correlation $4$ dB/ $0.95$ , fading correlation $0.9$ ; sensing RCS median $1$ m 2 , RCS std./correlation $3$ dB/ $0.98$ , shadowing std./correlation $3$ dB/ $0.95$ , fading correlation $0.9$ .
Communication	Minimum rate $R_{k}^{\min}=2$ Mbit/s; Markov on/off demand with initial-on $0.50$ , on $\to$ off/off $\to$ on probabilities $0.08/0.20$ , and lognormal on-demand median $5$ Mbit/s (log-std. $0.45$ ); equal-share scheduling.

TABLE I: Final experimental configuration. Learned-run values are taken from the effective configurations recorded in the final artifacts;

U[a,b]

denotes the continuous uniform distribution on

[a,b]

Policy	Return	Completed value	Sense cost	$\mathbf{E^{+}}$	RPS
CT-PPO	67.511	74.005	32.474	2.164	1.114
JC-PPO	66.576	74.326	38.751	2.382	1.034
SLA-Aware Greedy	65.663	72.678	35.076	2.512	1.081
Static Compatibility Merge	63.438	66.702	16.321	4.627	1.125
Greedy Incremental Cost	63.417	66.673	16.278	4.641	1.105
No Consolidation	62.998	66.366	16.843	4.722	1.000

TABLE II: Primary external macro results. Learned entries average five validation-selected training seeds; deterministic heuristics average matched external roots, and Random Valid is averaged within trace.

E^{+}

is positive constraint excess; RPS is accepted requests per created session.

Metric	Macro	Independent	Clustered
Return	$+0.934\ [0.702,1.164]$	$+0.827\ [0.573,1.072]$	$+1.042\ [0.752,1.329]$
Completed value	$-0.321\ [-0.660,0.023]$	$-0.583\ [-1.037,-0.148]$	$-0.059\ [-0.351,0.246]$
Sensing-resource cost	$-6.277\ [-7.625,-4.804]$	$-7.047\ [-8.984,-4.889]$	$-5.507\ [-6.578,-4.399]$
Positive constraint excess	$-0.219\ [-0.573,0.058]$	$+0.227\ [0.088,0.409]$	$-0.665\ [-1.371,-0.128]$
RPS	$+0.0806\ [0.0656,0.0954]$	$+0.0177\ [0.0134,0.0221]$	$+0.1434\ [0.1164,0.1701]$
Merge /episode	$+2.344\ [1.926,2.754]$	$+0.892\ [0.684,1.104]$	$+3.796\ [3.120,4.472]$

TABLE III: CT-PPO minus JC-PPO effects from validation-selected checkpoints. Entries are

\Delta

[95% hierarchical paired-bootstrap CI].

Fig. 3: Direct consolidation and sensing-resource behavior across arrival regimes. Points denote mean Merge / Create actions per episode, accepted requests per created session (RPS), and episode sensing-resource cost. Whiskers show percentile 95% intervals from a hierarchical bootstrap over five training seeds and 50 external roots for learned policies, and a root-level bootstrap over 50 roots for SLA-Aware Greedy.

Metric	Factorized-JC $-$ JC-PPO	CT-Reward $-$ Factorized-JC	CT-PPO $-$ CT-Reward
Return	$-0.099\ [-0.472,0.287]$	$+1.013\ [0.666,1.338]$	$+0.021\ [-0.143,0.209]$
Completed value	$-0.692\ [-1.272,-0.239]$	$+0.343\ [-0.028,0.842]$	$+0.028\ [-0.206,0.316]$
Sensing-resource cost	$-2.968\ [-7.034,-0.064]$	$-3.349\ [-6.233,0.265]$	$+0.039\ [-0.585,0.693]$
Positive constraint excess	$-0.016\ [-0.439,0.338]$	$-0.186\ [-0.421,0.025]$	$-0.016\ [-0.124,0.079]$
RPS	$+0.0063\ [-0.0089,0.0250]$	$+0.0625\ [0.0414,0.0818]$	$+0.0117\ [-0.0031,0.0290]$
Merge /episode	$+0.154\ [-0.344,0.752]$	$+1.864\ [1.250,2.448]$	$+0.326\ [-0.100,0.828]$

TABLE IV: Adjacent component-ablation effects. Each entry is the second method minus the first method,

\Delta

[95% hierarchical paired-bootstrap CI]. Only adjacent contrasts are used for attribution.

Metric	Low ( $0.06$ )	Nominal ( $0.08$ )	High ( $0.10$ )
CT-PPO return	$52.631$	$67.511$	$83.978$
JC-PPO return	$51.941$	$66.576$	$82.535$
Return	$+0.690\ [0.475,0.910]$	$+0.934\ [0.702,1.164]$	$+1.443\ [1.137,1.748]$
Completed value	$-0.275\ [-0.486,-0.092]$	$-0.321\ [-0.660,0.023]$	$-0.061\ [-0.579,0.428]$
Sensing-resource cost	$-4.828\ [-5.944,-3.613]$	$-6.277\ [-7.625,-4.804]$	$-7.521\ [-9.324,-5.685]$
Positive constraint excess	$+0.075\ [0.006,0.160]$	$-0.219\ [-0.573,0.058]$	$-0.748\ [-1.134,-0.390]$

TABLE V: Frozen-checkpoint arrival-load robustness. The load is the common scalar applied to the independent per-tenant arrival rate and clustered parent-event rate. Operating-point rows report mean return; effect rows are CT-PPO minus JC-PPO,

\Delta

[95% hierarchical paired-bootstrap CI].

Fig. 4: Validation dynamics over physical training slots. Curves are unsmoothed five-seed mean macro validation returns; shading spans the seedwise minimum–maximum range.

Trainable and deployed parameters
Method	Trainable	Prefix critic	Encoder–actor
JC-PPO	306,450	0	288,519
Factorized-JC	306,450	0	288,519
CT-Reward	306,450	0	288,519
CT-PPO	346,569	40,119	288,519
Mean inference latency (ms)

TABLE VI: Model footprint and batch-one CPU inference. Latencies are five-checkpoint-pair means over the same

500

environment-generated observations; actor-only actions were checked against the reference path before timing.

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Open paper AskPDF arXiv

Future integrated sensing and communication (ISAC) architectures separate the sensing entity (SE) that acquires measurements from the sensing function (SF) that performs inference, creating a need for compact, task-oriented feedback on the SE-SF interface. Forwarding the raw channel frequency response or full per-link delay-Doppler-azimuth-elevation (DDAE) tensor is prohibitively expensive, while peak-only reporting discards target-discriminative structure under clutter. We propose a learning-based coarse-to-fine sensing pipeline with candidate-latent feedback for single-target estimation. At the SE, a lightweight convolutional scorer produces a dense delay-Doppler proposal map from pilot-based OFDM channel estimates, and a learned encoder constructs K compact C-dimensional candidate tokens by fusing per-candidate azimuth-elevation patches, normalized position, and confidence cues. The latents are uniformly quantized post-training to b bits and transmitted under a finite budget B_fb = bKC + 18K + 16 bits to the SF, which performs cross-candidate refinement, reranking, and joint four-parameter estimation. On a ray-traced urban scene with static and dynamic clutter, three operating points in the (K, C, b) design space achieve 96.33-98.88% detection at 107-806 bytes per coherent processing interval, compression ratios of 1.2-9.2 x 10^4 over the 8-bit DDAE magnitude tensor, reducing the SE-SF interface from multi-Gbit/s to sub-Mbit/s rates. Cross-scene evaluation on an independent campus-scale environment achieves 98.79-99.50% detection and at-or-better angular accuracy without retraining, indicating that the learned representation captures target-relevant structure that transports across scenes of comparable or lower clutter density.

Abstract

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