BARProp: Buffer-Aided RMSProp

• The paper demonstrates that BARProp improves convergence speed by about 4× and enhances localization accuracy compared to standard RMSProp and heavy convex relaxations.
• BARProp is a buffer-aided adaptive optimization algorithm that replaces a fixed decay factor with a dynamic, coordinatewise decay derived from a short history of squared gradients.
• The method significantly reduces memory usage (using less than 15% of competing methods) and computational cost, making it ideal for resource-constrained IoT localization.

Searching arXiv for the BARProp paper and closely related RMSProp work to ground the article in current literature. I found the BARProp paper on arXiv together with related RMSProp literature on adaptive step sizing, stability, and memory-augmented variants, which I’ll use to situate the method technically (Abanto-Leon et al., 29 Sep 2025, Robles-Kelly et al., 2022, Bensaid et al., 2024, Dimitrieski et al., 16 Mar 2026). Buffer-Aided RMSProp (BARProp) is a lightweight adaptive optimization algorithm for received-signal-strength (RSS)-based indoor localization in IoT and wireless sensor network settings. It is presented as a model-based alternative to computationally heavy convex relaxations such as SDP and SOCP, to more expensive evolutionary methods such as DEOR, and to scenario-specific fingerprinting or deep-learning approaches that require offline data collection. BARProp retains the RMSProp principle of normalizing updates by a smoothed estimate of recent squared gradients, but replaces the fixed decay factor with a coordinatewise adaptive one derived from a short gradient-history buffer. In the reported evaluations, it requires less than 15% of the memory used by state-of-the-art methods and delivers at least a fourfold improvement in convergence speed while improving localization accuracy on both simulated and real data (Abanto-Leon et al., 29 Sep 2025).

1. Problem formulation and intended application domain

BARProp is designed for RSS-based indoor localization when access points or anchor nodes are inexpensive, power-limited, and unable to support heavy optimization pipelines. The target problem is maximum-likelihood estimation of a node position from RSS measurements under a path-loss model, a setting in which the objective is highly nonconvex and susceptible to poor local minima. The paper explicitly frames BARProp against several families of alternatives: convex relaxations such as SDP and SOCP, evolutionary search such as DEOR, and data-driven fingerprinting or deep learning pipelines. The rationale is that the first group is often too computationally demanding for embedded deployment, the second incurs additional tuning and memory costs, and the third requires scenario-specific offline collection that may be impractical in low-cost IoT settings (Abanto-Leon et al., 29 Sep 2025).

The localization model assumes a two-dimensional unknown target position

$\mathbf{x}=[x_1,x_2]^\mathrm{T},$

with $N$ anchors at known positions $\mathbf{s}_n$. For anchor $n$, the RSS observation obeys

$$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$

where $P_0$ is transmit power, $\gamma$ is the path-loss exponent, and $v_n\sim \mathcal{N}(0,\sigma_n^2)$ is log-shadowing noise. From this model, the paper formulates a weighted maximum-likelihood estimator with intended objective

$$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$

Because this cost is nonconvex, standard first-order methods may converge slowly or unstably, especially when anchor geometry is poor or shadowing noise is large. BARProp is therefore proposed as a localization-specific optimizer rather than as a generic reimplementation of RMSProp. Its design goal is to preserve low-order computational cost and small state while making the adaptive denominator respond more appropriately to whether recent gradients appear stable or volatile.

2. Core optimization mechanism

The defining feature of BARProp is the replacement of RMSProp’s fixed decay factor with a coordinatewise adaptive decay factor computed from a short FIFO-style buffer of recent squared gradients. In standard RMSProp, the second-moment estimate keeps using a fixed exponential forgetting rate, so stale gradients can continue to influence the denominator after they have ceased to be informative. BARProp attempts to detect this condition indirectly by monitoring the spread of recent squared-gradient energy (Abanto-Leon et al., 29 Sep 2025).

The algorithm begins with an initialization stage intended to reduce sensitivity to poor local starts. It samples $U$ feasible candidate positions

$N$0

in the search region and selects

$N$1

This initialization is part of the optimizer rather than a separate localization heuristic.

At iteration $N$2, the manuscript gives the gradient in a typographically imperfect form. The intended quantity is the gradient of the weighted squared-residual objective above. BARProp then follows the usual RMSProp pattern: square the gradient elementwise, update a coordinatewise exponential moving average, and normalize the descent step by the square root of that accumulator plus a small stability term. The intended position update is

$N$3

where $N$4 is the learning rate, $N$5 is a small numerical-stability vector, and $N$6 is the smoothed squared-gradient accumulator.

The new part lies in the decay factor. BARProp maintains a buffer

$N$7

whose rows correspond to coordinates $N$8 and $N$9, and whose columns store the most recent $\mathbf{s}_n$0 squared gradients in cyclic order. With buffer index

$\mathbf{s}_n$1

the current squared gradient is written into column $\mathbf{s}_n$2. From the buffer contents, BARProp computes the coordinatewise maxima and minima

$\mathbf{s}_n$3

then forms

$\mathbf{s}_n$4

and finally defines the adaptive decay factor as

$\mathbf{s}_n$5

The corresponding second-moment recursion is

$\mathbf{s}_n$6

where the “squared gradient” is computed elementwise as

$\mathbf{s}_n$7

The paper interprets this mechanism as a speed–stability switch. If recent squared gradients in the buffer change little, then $\mathbf{s}_n$8 is small, $\mathbf{s}_n$9 approaches $n$0, and the method reacts more strongly to current gradients. If buffered energies vary substantially, $n$1 decreases toward its lower bound, producing heavier smoothing and greater update stability. The wording around “resetting memory” is explicitly described as somewhat nonstandard relative to conventional EMA intuition, but the intended operational mechanism is clear: gradient stability increases responsiveness, whereas gradient volatility increases damping.

3. Full algorithmic workflow and feasibility control

BARProp augments the adaptive RMSProp core with a bounded search mechanism. This is not an objective regularizer; the paper describes it as a feasibility safeguard intended to keep iterates inside the admissible localization region, especially in early iterations when normalized steps may still be large (Abanto-Leon et al., 29 Sep 2025).

After the normalized update, each coordinate is clipped to the search box: $n$2 If the raw update exits the feasible box, BARProp adds a small corrective perturbation,

$n$3

and enforces

$n$4

At pseudocode level, the workflow is:

• sample $n$5 feasible initial positions and choose the one with minimum localization cost;
• initialize $n$6 and the $n$7 gradient buffer $n$8;
• for $n$9, compute the gradient, square it elementwise, insert it into the cyclic buffer, compute $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$0 and $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$1, derive $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$2, set $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$3, update $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$4, apply the normalized step, and then apply the bounding correction if required;
• stop when the change between successive estimates is below $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$5 or when the iteration count reaches $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$6.

The reported experimental settings use

$$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$7

$$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$8

For plain RMSProp, the paper keeps the same settings except $$P_n = P_0 - 10\gamma \log_{10}\left\| \mathbf{x} - \mathbf{s}_n \right\|_2 + v_n,$$9.

A practical implication is that BARProp is intentionally narrow in scope: it is tailored to a two-coordinate localization parameterization, and its buffer is correspondingly $P_0$0. This suggests that the method’s memory efficiency partly derives from the small dimensionality of the localization state, although the paper’s central claim is that the dynamic decay mechanism itself—not merely the 2D setting—provides the favorable speed–stability trade-off.

4. Complexity and memory characteristics

BARProp is explicitly marketed as a resource-constrained optimizer. Its theoretical computational complexity is reported as

$P_0$1

where $P_0$2 is the number of random initialization points, $P_0$3 the number of anchors, and $P_0$4 the maximum number of iterations. Since convergence may occur before $P_0$5, this is a worst-case upper bound. The paper contrasts this with RMSProp at $P_0$6, DEOR at $P_0$7, ML-true at $P_0$8, SOCP at $P_0$9, and SDP at $\gamma$0 (Abanto-Leon et al., 29 Sep 2025).

Memory usage is one of the paper’s central claims. The algorithmic memory footprint is stated as approximately

$\gamma$1

for BARProp, versus $\gamma$2 bytes for RMSProp, $\gamma$3 bytes for DEOR, $\gamma$4 bytes for ML-true, approximately $\gamma$5 for SDP, and approximately $\gamma$6 for SOCP. Under the reported setting $\gamma$7 and DEOR’s $\gamma$8, BARProp uses about 14.2% of DEOR’s memory, which is the quantitative basis for the statement that it uses less than 15% of the memory of prior state-of-the-art methods.

Method	Complexity	Memory footprint
BARProp	$\gamma$9	$v_n\sim \mathcal{N}(0,\sigma_n^2)$0 bytes
RMSProp	$v_n\sim \mathcal{N}(0,\sigma_n^2)$1	$v_n\sim \mathcal{N}(0,\sigma_n^2)$2 bytes
DEOR	$v_n\sim \mathcal{N}(0,\sigma_n^2)$3	$v_n\sim \mathcal{N}(0,\sigma_n^2)$4 bytes
ML-true	$v_n\sim \mathcal{N}(0,\sigma_n^2)$5	$v_n\sim \mathcal{N}(0,\sigma_n^2)$6 bytes
SDP	$v_n\sim \mathcal{N}(0,\sigma_n^2)$7	$v_n\sim \mathcal{N}(0,\sigma_n^2)$8
SOCP	$v_n\sim \mathcal{N}(0,\sigma_n^2)$9	$$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$0

These formulas are algorithmic memory and complexity descriptions rather than end-to-end system costs. The paper’s interpretation is that BARProp’s short gradient buffer avoids the population storage of evolutionary methods and the large matrix variables of convex relaxations. A plausible implication is that the method is most attractive when the optimization routine must run directly on access points or anchor-class hardware, rather than on a more capable centralized processor.

5. Empirical evaluation

The empirical study combines simulation and real measurements. In simulation, RSS is generated from the path-loss model with $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$1 dBm, $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$2, and $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$3 dB. The performance metric is RMSE, intended as the standard root mean square position error over $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$4 Monte Carlo runs. Two anchor layouts are considered in a $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$5 m area: a homogeneous deployment where the target lies inside the anchor convex hull, and a non-homogeneous deployment where anchors occupy only part of the area and the target is outside their convex hull. The number of anchors is varied over $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$6 (Abanto-Leon et al., 29 Sep 2025).

Across these simulations, all methods degrade as shadowing noise increases, but BARProp and DEOR are reported as less sensitive, especially in the non-homogeneous-anchor case. At $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$7 dB, the reduction in localization accuracy when moving from homogeneous to non-homogeneous deployment is 23.95% for BARProp, 24.56% for DEOR, 38.37% for ML-true, 39.03% for RMSProp, 64.22% for SDP, and 64.23% for SOCP. BARProp is therefore presented as among the most robust methods under degraded anchor geometry. When the number of anchors increases, all methods improve; BARProp, DEOR, and ML-true are reported as strongest in absolute accuracy, with BARProp clearly outperforming RMSProp, SDP, and SOCP across the tested range. The manuscript text around the $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$8 case is truncated, but it reports BARProp improving localization accuracy by about 15–16% relative to several baselines.

The runtime results reinforce the algorithm’s positioning. In the varying-anchor simulation table, average running times are: BARProp 0.93 ms, DEOR 4.48 ms, ML-true 3.59 ms, RMSProp 0.78 ms, SDP 315.92 ms, and SOCP 413.92 ms. Hence BARProp is approximately 5× faster than DEOR, 4× faster than ML-true, 339× faster than SDP, and 444× faster than SOCP. RMSProp is slightly faster, but the paper pairs this with lower localization accuracy. The text also states that the runtime-versus-number-of-anchors figure shows BARProp as the least computationally demanding among all evaluated methods, consistent with its linear scaling.

The real-world experiment uses a $$f(\mathbf{x})=\sum_{n=1}^{N}\frac{1}{\sigma_n^2}\left(P_n-P_0+10\gamma\log_{10}\|\mathbf{x}-\mathbf{s}_n\|_2\right)^2.$$9 indoor environment from prior work, with 5 anchors and 27 predefined target positions. For each anchor-target pair, 1000 RSS measurements are collected; each localization trial uses one sampled RSS per anchor, repeated 1000 times. Performance is reported through the CDF of localization error $U$0. BARProp yields the best CDF: error $U$1 m in 82% of trials, compared with probabilities below 72% for DEOR, 70% for ML/ML-true, 70% for RMSProp, and 61% for the convex baselines. Real-experiment runtimes are 0.66 ms for BARProp, 3.23 ms for DEOR, 2.70 ms for ML-true, 0.41 ms for RMSProp, 463.90 ms for SDP, and 524.10 ms for SOCP. This corresponds to about 4.91× speedup over DEOR, 4.09× over ML-true, 703.89× over SDP, and 795.23× over SOCP.

Taken together, these results support the paper’s principal empirical claim: BARProp offers a better speed–accuracy balance than the nearest accurate competitors, while remaining much lighter than convex solvers. The evidence is empirical rather than theoretical, but it is unusually concrete for a localization-specific optimizer, because both simulation and real data are included.

6. Relationship to RMSProp variants, theoretical context, and limitations

BARProp is explicitly framed as an enhancement of RMSProp. Standard RMSProp uses a fixed decay factor in its squared-gradient exponential moving average. BARProp preserves the coordinatewise normalization structure but substitutes a dynamic, coordinatewise decay factor derived from a finite buffer of recent squared gradients. In that sense, its closest parent method is plain RMSProp, not SGD, momentum, Adam, or Adadelta (Abanto-Leon et al., 29 Sep 2025).

Within the broader RMSProp literature, BARProp occupies a distinct point in the design space. The Barzilai–Borwein integration method of “Incorporating the Barzilai-Borwein Adaptive Step Size into Sugradient Methods for Deep Network Training” uses a minimal two-step history—previous displacement and previous gradient—to apply a layerwise scalar BB factor on top of Adagrad or RMSProp, but it does not use a finite multistep squared-gradient buffer, and it does not provide a direct RMSProp-versus-BB-RMSProp benchmark (Robles-Kelly et al., 2022). “Adaptive Extremum Seeking Control via the RMSprop Optimizer” embeds RMSProp-like normalization in continuous-time extremum-seeking control through a low-pass state for squared gradient estimates, which is a memory mechanism, but not an explicit finite-history buffer (McNamee et al., 2024). “Vprop: Variational Inference using RMSprop” reinterprets RMSProp’s second-moment state as a posterior-precision surrogate in Bayesian deep learning, showing that RMSProp buffers can serve representational as well as optimization roles (Khan et al., 2017). More recent theory for standard RMSProp analyzes global asymptotic stability under strong-convexity and smoothness assumptions (Dimitrieski et al., 16 Mar 2026) or iterate convergence under adaptive backtracking and Łojasiewicz assumptions (Bensaid et al., 2024). These works are relevant as templates for analysis, but none directly establish convergence guarantees for BARProp’s buffer-driven dynamic decay.

Several limitations are explicit in the BARProp paper. The convergence and stability argument is heuristic plus empirical; no formal convergence proof is given. The method remains a heuristic optimizer for a nonconvex objective. Its performance depends on hyperparameters such as $U$2, $U$3, $U$4, and the bounding perturbation range. The manuscript also contains typographical issues in the objective, gradient, and update equations, although the intended forms are sufficiently clear to reconstruct the method. There are no explicit ablation tables isolating the effect of the buffer mechanism or the dynamic decay factor; the comparison to plain RMSProp functions as an implicit ablation. The paper therefore argues, rather than proves, that the buffer-driven adaptive decay is the key ingredient behind the improved trade-off between speed and stability.

The same section of the paper identifies future directions: adaptive buffer length $U$5, adaptive learning rate $U$6, distributed implementations, and extension to three-dimensional or multimodal measurements. These are consistent with the method’s current status. BARProp is best understood not as a general-purpose optimizer, but as a buffer-augmented, dynamically decayed RMSProp variant engineered for RSS localization under severe computational and memory constraints.