PUCS: Probing-Augmented User-Centric Selection

• PUCS is a two-stage framework where initial probing gathers side information before performing user-centric selection to mitigate uncertainty.
• The formal model integrates probing overhead, stochastic resource assignments, and guarantees constant-factor regret bounds using greedy approximation.
• PnPSelect implements PUCS in smart-home settings, leveraging UWB sensing and geometric localization to enable plug-and-play IoT device selection.

Searching arXiv for the specified PUCS papers and related context. Probing-Augmented User-Centric Selection (PUCS) denotes a two-stage selection paradigm in which a decision-maker first acquires targeted side information through probing and then performs a user-centered selection or assignment using that information. In the formal sequential setting, PUCS models costly information acquisition before assigning $K$ plays to $M$ arms under uncertainty in both resources and rewards. In a concrete smart-home instantiation, PUCS is operationalized by PnPSelect, where Ultra-wideband (UWB) measurements gathered during a natural pointing gesture serve as the probing signal and the user’s pointing act serves as the user-centric selection mechanism (Xu et al., 27 Jul 2025, Chang et al., 5 Nov 2025).

1. Conceptual scope and dual usage

PUCS appears in two closely connected senses. First, it is a formal framework for sequential decision-making with information acquisition: a learner probes a subset of arms, observes side information on resources and rewards, and then allocates plays. Second, it is a systems concept instantiated by PnPSelect, where UWB ranging and angle observations collected during a pointing gesture are transformed into device selection and registration without installing dedicated radios on each IoT device. In both senses, the defining structure is identical: probing precedes selection, probing is not free, and the selection rule is centered on the user’s immediate objective rather than on static infrastructure-centric identification (Xu et al., 27 Jul 2025, Chang et al., 5 Nov 2025).

Aspect	Formal PUCS	PnPSelect instantiation
Probing object	Subset of arms	UWB trajectory during pointing
Side information	Resources and rewards	Distance $d$, azimuth $\phi$, elevation $\theta$
Selection object	Assignment of $K$ plays to $M$ arms	Selection of a registered IoT device
Cost model	Probing overhead $\alpha(|S_t|)$	Sub-second gesture and lightweight computation
User-centric element	Final allocation after probe	Natural phone/watch pointing
Registration mechanism	Not explicit in base theory	Two-point geometric localization

This dual usage is important because it prevents an overly narrow reading of PUCS as either a purely abstract bandit model or a purely embodied interaction method. The formal work establishes the decision-theoretic structure, approximation guarantees, regret bounds, and lower bounds. The PnPSelect work shows that the same structure can govern room-scale interactive selection using commodity UWB devices.

2. Formal sequential model

In the formalization, time proceeds over a horizon $t = 1,2,\ldots,T$. The system contains arms $[M] := \{1,2,\ldots,M\}$ and plays $M$0. At each round, each play is assigned to exactly one arm, while multiple plays may be assigned to the same arm. Each arm $M$1 has a stochastic number of resource units $M$2, distributed i.i.d. across rounds and arms with PMF $M$3. If play $M$4 assigned to arm $M$5 receives one resource unit, the reward is $M$6, an i.i.d. sample from an unknown distribution with mean $M$7 and CDF $M$8 (Xu et al., 27 Jul 2025).

The assignment at round $M$9 is represented by sets $d$0. If arm $d$1 is probed, the learner observes exact within-round realizations $d$2 and $d$3. The total realized reward from that arm is the sum of the top $d$4 realized rewards among the assigned plays, reflecting the rule that higher-reward plays are served first when resources are limited. If arm $d$5 is not probed, only the distributional information is available, and the expected total reward is computed from the sorted expected rewards $d$6 and the PMF $d$7.

Probing is budgeted. At each round, the learner chooses a probing set $d$8 with $d$9. The probing overhead is modeled multiplicatively by a non-decreasing function $\phi$0, with $\phi$1 and $\phi$2. The round reward is therefore

$\phi$3

For the offline setting with known distributions, the expected value of probing set $\phi$4 is

$\phi$5

For the online setting with unknown distributions, performance is measured through $\phi$6-approximation regret,

$\phi$7

where $\phi$8 is the offline-optimal probing set at round $\phi$9. The framework assumes i.i.d. resources and rewards, independence between $\theta$0 and $\theta$1, a bounded probing budget, and general reward distributions rather than Bernoulli-only models.

3. Offline approximation and online learning

The offline optimization over probing sets is computationally hard, so the analysis introduces a surrogate decomposition. The probed-only value $\theta$2 is the expected optimal assignment value when only the arms in $\theta$3 are considered after probing. The unprobed-only value $\theta$4 is the optimal expected assignment value over the arms in $\theta$5 without probing. A key inequality is

$\theta$6

The paper further establishes that $\theta$7 is monotonically decreasing in $\theta$8, whereas $\theta$9 is monotonically increasing and submodular. These structural facts enable an Offline Greedy Probing algorithm that iteratively adds the arm with largest marginal gain in $K$0, then selects the greedy set that maximizes $K$1, with a final comparison against the no-probing value $K$2 (Xu et al., 27 Jul 2025).

The resulting constant-factor guarantee is

$K$3

The argument combines the upper bound above, monotone-submodular greedy approximation of $K$4, and the multiplicative probing overhead. The reported complexity is $K$5 when evaluating the surrogate through an assignment solver, or $K$6 when using sampling with $K$7 realizations.

For the online setting, the paper introduces OLPA, a stochastic combinatorial bandit algorithm. OLPA maintains empirical resource PMFs $K$8, empirical reward means $K$9, empirical reward CDFs $M$0, counts $M$1, and UCB-style confidence radii $M$2. At round $M$3, OLPA first runs Offline Greedy Probing on current estimates to obtain $M$4, then probes those arms to observe $M$5, and finally solves the assignment problem using exact realizations for probed arms and optimistic estimates $M$6 with $M$7 for unprobed arms.

Its regret guarantee is

$M$8

more precisely an $M$9 bound with explicit dependence on $\alpha(|S_t|)$0, $\alpha(|S_t|)$1, $\alpha(|S_t|)$2, $\alpha(|S_t|)$3, and maxima of $\alpha(|S_t|)$4. A lower bound of $\alpha(|S_t|)$5 is proved by reduction to single-play MAB, showing that the upper rate is tight up to logarithmic factors. The paper also notes that when $\alpha(|S_t|)$6, the leading constant in the $\alpha(|S_t|)$7 term is strictly smaller than in the non-probing variant because the probed information shrinks the unprobed contribution.

4. Geometric and systems instantiation in PnPSelect

PnPSelect operationalizes PUCS in smart-home interaction by mapping probing to UWB sensing during a natural pointing gesture and mapping selection to the identification of a target IoT device from a stored set of 3D coordinates. The system assumes one fixed UWB anchor with known position and orientation, defining an anchor coordinate system $\alpha(|S_t|)$8, and a user device such as a smartphone or smartwatch equipped with UWB and IMU hardware. The core algorithm uses UWB rather than magnetometer/IMU orientation, because indoor magnetic distortion and handset tilts degrade orientation-based pointing accuracy (Chang et al., 5 Nov 2025).

The hardware and software pipeline is explicitly modular. UWB acquisition through Apple Nearby Interaction or the Android UWB API streams $\alpha(|S_t|)$9, $t = 1,2,\ldots,T$0, and $t = 1,2,\ldots,T$1 at about $t = 1,2,\ldots,T$2 Hz. These are converted into 3D positions

$t = 1,2,\ldots,T$3

A Kalman filter smooths the position stream, after which PCA is applied to the smoothed trajectory samples $t = 1,2,\ldots,T$4 to extract the dominant motion vector $t = 1,2,\ldots,T$5. The optimization criterion is

$t = 1,2,\ldots,T$6

The first principal component is treated as the pointing direction; the second and third components capture lateral jitter and are discarded.

Selection is then posed as directional matching against registered devices. For a device $t = 1,2,\ldots,T$7 with stored position $t = 1,2,\ldots,T$8, the unit ray from the current phone position is

$t = 1,2,\ldots,T$9

The gesture-level directional match score is

$[M] := \{1,2,\ldots,M\}$0

equivalently minimizing

$[M] := \{1,2,\ldots,M\}$1

The selected device is $[M] := \{1,2,\ldots,M\}$2, or equivalently the device with highest $[M] := \{1,2,\ldots,M\}$3. If the top two scores are within a small margin, the system presents multiple candidates instead of auto-selecting.

PnPSelect also defines a lightweight registration procedure requiring two pointing operations from distinct user positions. With positions $[M] := \{1,2,\ldots,M\}$4 and direction vectors $[M] := \{1,2,\ldots,M\}$5, the two pointing lines are

$[M] := \{1,2,\ldots,M\}$6

Defining

$[M] := \{1,2,\ldots,M\}$7

the least-squares solution is

$[M] := \{1,2,\ldots,M\}$8

and the device position is estimated as the midpoint of the shortest connector segment,

$[M] := \{1,2,\ldots,M\}$9

For stable localization, the paper advises angular separation greater than $M$00 between the two pointing directions; in practice, moving two steps, corresponding to $M$01 m at $M$02 m anchor distance, is sufficient.

The overall end-to-end flow is therefore: point, probe, estimate, select, and optionally register. A short gesture of approximately $M$03–$M$04 cm displacement is sufficient, no per-device radio installation is required, and the computation consists primarily of Kalman filtering, PCA, dot products, and a constant-size least-squares solve.

5. Empirical results and comparative position

In the formal PUCS setting, experiments are conducted on NYYellowTaxi 2016 and Chicago Taxi Trips 2016. Pickup locations are discretized into $M$05 grid cells, passenger counts define the PMFs $M$06, vehicles are pre-sampled and fixed across experiments, and rewards are based on normalized Manhattan distance to pickups. The baselines are Non-Probing (OnLinActPrf), RR (Random probing, Random assignment), and GR (Greedy probing, Random assignment). The evaluation metric is $M$07-approximation cumulative regret, with $M$08 computed by exhaustive search for the reported settings (Xu et al., 27 Jul 2025).

Across the reported configurations, OLPA consistently attains the lowest cumulative regret. In Chicago (b), with $M$09, $M$10, and Bernoulli rewards, OLPA achieves $M$11 regret at $M$12 steps, compared with Non-Probing at $M$13, GR at $M$14, and RR at $M$15. In Chicago (a), with $M$16, $M$17, and Bernoulli rewards, the corresponding figures are $M$18 for OLPA and $M$19 for Non-Probing. In Chicago (c), with a general discrete reward distribution, OLPA reports $M$20, compared with $M$21 for Non-Probing. In NYYellowTaxi (d), with $M$22, $M$23, and the general distribution, OLPA reaches $M$24, while Non-Probing reaches $M$25.

In the PnPSelect system evaluation, pointing direction estimation is measured across $M$26 directions in the XY and YZ planes. The median angular error is approximately $M$27–$M$28, with $M$29th percentile error approximately $M$30–$M$31. Errors remain below $M$32 across all directions, with only slight increase at longer distances or larger azimuth angles relative to the anchor. Gesture displacement matters: gestures of at least $M$33 cm yield less than $M$34 error, whereas $M$35 cm gestures yield about $M$36. Gesture speed from $M$37 to $M$38 cm/s shows less than $M$39 error, indicating little sensitivity to velocity (Chang et al., 5 Nov 2025).

The paper translates this angular performance into spatial resolution. With $M$40 direction error, two devices separated by $M$41 cm at $M$42 m are theoretically distinguishable. The measured resolution for PnPSelect is $M$43 and $M$44 cm at device distances $M$45 m, outperforming distance-change and AoA-only baselines, which require per-device radios. Device registration achieves mean localization error below $M$46 m for all six users in a bedroom, and the error stabilizes below $M$47 m once the angular separation between the two pointing lines exceeds $M$48.

Real-world selection accuracy is reported in four environments—two bedrooms, a classroom, and a meeting room—with $M$49 devices per environment, six participants, $M$50 user locations, and five trials per device and location. The resulting accuracies are $M$51, $M$52, $M$53, and $M$54. The principal failure mode occurs when devices are very close or nearly collinear with the pointing direction. Candidate presentation is therefore used as an explicit ambiguity-management mechanism rather than forcing a brittle auto-selection decision.

These empirical results occupy different levels of abstraction but point in the same direction. In the sequential theory, probing improves regret relative to non-probing and random baselines. In the UWB system, probing through a short gesture produces robust room-scale selection without per-device radios. This suggests that PUCS is not merely a modeling convenience; it is a reusable design pattern in which modest, targeted information acquisition can materially improve downstream selection quality.

6. Assumptions, limitations, and research directions

The formal PUCS framework assumes stationarity and independence: $M$55 and $M$56 are i.i.d. across rounds, independent across arms, and independent of each other. Probing reveals exact within-round realizations for probed arms, whereas unprobed arms remain distributional within the round. The probing budget $M$57 is fixed per round, and the cost is summarized by a scalar non-decreasing overhead $M$58. The main algorithmic limitation is computational: repeated assignment solving yields $M$59-scale subroutines, which are polynomial but potentially significant in large systems (Xu et al., 27 Jul 2025).

PnPSelect makes a different set of assumptions. It requires a fixed anchor with known pose, commodity user devices with UWB support, and previously registered 3D device coordinates in the anchor coordinate frame. It does not require per-device calibration or per-device radios, but severe NLoS between anchor and user device can degrade angle estimates. Accuracy also degrades at room edges, although the paper reports that selection remains above $M$60 across anchor placements. Extremely close devices below the spatial resolution of the direction estimator remain problematic; the mitigation is to present top candidates for confirmation rather than to force a single automatic output (Chang et al., 5 Nov 2025).

Several misconceptions are explicitly ruled out by the two papers. PUCS does not treat probing as free; overhead is central both in the formal model and in practical system design. PnPSelect is not an IMU-orientation method with UWB added for convenience; its core estimator intentionally avoids relying on magnetometer/IMU heading because indoor magnetic distortion and device tilt degrade accuracy. Nor is PUCS inherently tied to per-object instrumentation: in PnPSelect, the plug-and-play claim rests precisely on zero hardware per device and a single anchor. Likewise, the comparison to vision-based methods is framed in terms of environmental robustness: computer vision struggles in low light and with visually similar devices, whereas UWB-based pointing is agnostic to appearance and lighting.

The research directions identified in the papers are correspondingly domain-specific. For formal PUCS, proposed extensions include non-stationary PUCS, contextual PUCS, adversarial variants, dynamic $M$61, richer resource constraints, per-arm probing costs, tighter constants, instance-dependent bounds, and improved large-scale algorithms. For PnPSelect, proposed improvements include multi-anchor fusion, anchor self-calibration via TDoA/AoA, optional IMU fusion for micro-motion modeling, improved magnetometer calibration, combined vision/RF disambiguation, and privacy/security mechanisms around UWB permissions, user consent, device registration, and control.

Taken together, these developments indicate a broad interpretation of PUCS. At the abstract level, it is a theory of probe-then-select decision-making under dual uncertainty. At the systems level, it is a deployable interaction pattern in which short, low-effort user actions generate signal-rich probes that support accurate selection. A plausible implication is that future PUCS research will increasingly connect these levels, using formal probing-and-assignment models to reason about embodied interactive systems whose measurements, costs, and ambiguities are explicitly user-facing.