AnchorOPT: Methods for Anchor-Based Optimization

• AnchorOPT is an umbrella term for three distinct ML frameworks that leverage anchor structures to stabilize learning and enhance performance.
• In dynamic prompt learning, it optimizes anchor tokens and position assignments, yielding improved cross-domain adaptability and superior generalization.
• Adaptive anchor box optimization uses Bayesian sub-sampling and SMC to efficiently tune hyperparameters, resulting in notable mAP gains in object detection.

AnchorOPT refers to three distinct methodologies introduced under the same moniker but addressing separate—yet anchor-centric—optimization paradigms in machine learning: (1) anchored direct preference optimization for robust preference learning, (2) dynamic anchor-based prompt learning for large vision-LLMs, and (3) adaptive anchor box optimization for object detection architectures. Each variant exploits anchor structures to yield measurable empirical gains, but the technical approaches, objectives, and applications differ fundamentally across their respective subfields.

1. AnchorOPT in Direct Preference Optimization

AnchorOPT, formalized as Anchored Direct Preference Optimization (ADPO), is a single-stage, reference-policy-anchored, and groupwise preference-optimization framework that extends Direct Preference Optimization (DPO) by introducing soft preferences, arbitrary anchoring, and listwise modeling (Zixian, 21 Oct 2025).

Core Objective Formulation

The ADPO framework generalizes the conventional DPO pairwise objective by incorporating a frozen reference policy $\pi_{\mathrm{ref}}$, which acts as an anchor to stabilize training via groupwise shift invariance and implicit Kullback–Leibler (KL) regularization:

$$\mathcal{L}_{\mathrm{ADPO}}(\theta) = -\,\mathbb{E}_{(x,i,j)\sim D}\Bigl[ p_{ij}\log\frac{\pi_\theta(y_i|x)}{\pi_{\mathrm{ref}}(y_i|x)} + (1-p_{ij})\log\frac{\pi_\theta(y_j|x)}{\pi_{\mathrm{ref}}(y_j|x)} \Bigr] + \mathrm{const.}$$

Here, $p_{ij}$ denotes the soft teacher-supplied pairwise preference probability, and log-ratios to the reference yield geometric invariance and regularization effects (confirmed in Lemmas 4.2–4.3).

Listwise Extension

ADPO extends to groupwise (listwise) settings via Plackett–Luce distributions. Teacher-generated lists are converted to target distributions $q(i\mid S_x)$ with temperature-scaled reward transforms (raw, rank-Gaussian, or kernel density estimate–CDF–logit smoothing), while the student’s anchored prediction $\tilde p_\theta(i\mid S_x)$ incorporates log-odds shifts to the reference policy. This enables robust learning even under adversarial or heavy-tailed label noise.

Special Cases Contained

• Hard labels, no anchor: reduces to standard DPO.
• Soft preferences, no anchor: recovers Bradley–Terry cross-entropy.
• Listwise, top-1 target, anchor-free: matches Top-1-vs-Rest cross-entropy formulation.

Empirical Findings

ADPO demonstrates superior robustness and sample efficiency:

• In contextual bandit settings (256-parameter models), anchored Soft-DPO improves WinMass by 38–63% over baseline DPO under Gaussian-mixture preference noise.
• Under Student-t noise (heavy-tailed, $\nu=1.5$), KDE-anchored ADPO achieves WinMass = 0.68 vs. 0.32 (112% relative gain).
• In sequential reinforcement learning (CartPole, LunarLander, Acrobot), the anchored approach improves mean return by 15–29% under label noise and displays only moderate sensitivity to hyperparameters.

2. AnchorOPT for Dynamic Prompt Learning

AnchorOPT has also been developed as a dynamic anchor-based prompt learning framework tailored for CLIP-like vision-LLMs, addressing limitations of fixed textual anchors and rigid prompt structures (Li et al., 26 Nov 2025).

Motivation and System Overview

Traditional prompt learning approaches (e.g., CoOp) rely on manually chosen textual anchor tokens and fixed anchor–soft token layouts, baking in human bias and leading to sub-optimal cross-task and cross-domain adaptation. AnchorOPT advances this line via:

• Learning anchor token values dynamically from LLM-generated category descriptions.
• Introducing a learnable position-assignment matrix for token ordering optimization, parameterized and trained via Gumbel-Softmax for differentiable and adaptive arrangements across tasks and stages.

Two-Stage Training

1. Anchor Sequence Learning: Optimize a sequence of anchor token embeddings $\{\mathbf{a}_i\}_{i=1}^N$ to minimize the mean-squared error between the anchor-sequence encoding and category description embeddings as processed by the frozen CLIP text encoder.
2. Soft Token and Position Optimization: With anchors frozen, jointly optimize the soft prompt tokens and the position matrix that governs anchor–soft token permutations via classification and knowledge-distillation–style KL loss terms.

Empirical Results

• AnchorOPT, as a plug-and-play module integrated with prompt learning methods like CoOp, boosts the base–novel harmonic mean (across 11 datasets) to 78.68 (compared to 71.66 for CoOp and 74.65 for ATPrompt).
• Ablations show that adaptive anchor and position learning independently and jointly improve generalization; AnchorOPT peaks with a single learnable anchor and is competitive even without explicit “anchor” tokens.
• In cross-dataset and domain generalization, AnchorOPT maintains consistent accuracy increases ($+3.05$ on cross-dataset HM, $+1.51$ on ImageNet→IN-V2/S/A/R domain transfer).

3. AnchorOPT in Adaptive Anchor Box Optimization

Under the variant termed “AABO,” AnchorOPT designates an anchor box optimization strategy for object detectors, particularly those employing feature-pyramid networks (FPNs) (Ma et al., 2020).

Hyperparameter Problem Formalization

Anchors (count, scale, aspect ratio per level) are treated as black-box hyperparameters:

$$x = (n_1, \{s_1\}, \{r_1\}, ..., n_L, \{s_L\}, \{r_L\})$$

$$x^* = \arg\min_{x \in \mathcal{X}} -\mathrm{mAP}(x)$$

The search domain is a hybrid of continuous (scales/ratios) and discrete (anchor counts) variables, reflecting granularity at each FPN level.

Bayesian Sub-sampling Optimization

AABO combines Tree-Parzen Estimator (TPE)–based Bayesian optimization with Sub-sample Mean Comparison (SMC) allocation. TPE models densities over "good" and "bad" anchor setups, proposing new configurations maximizing the density ratio. SMC dynamically allocates further training resources only to configurations statistically superior to the incumbent leader, providing efficient early stopping and resource allocation.

Search Space and Integration

For COCO with FPN, empirical bounds are derived per feature pyramid level (see Table below):

Level	n range	scale bounds	ratio bounds
1	5–12	[3.0, 15.0]	[0.25, 4.0]
2	4–10	[4.0, 12.0]	[0.3, 3.0]
3	4–8	[4.0, 12.0]	[0.4, 2.5]
4	3–7	[5.0, 15.0]	[0.5, 3.0]
5	3–6	[5.0, 12.0]	[0.7, 2.5]

Integration into frameworks such as MMDetection and Detectron2 is via direct overrides of per-level anchor generator parameters.

Empirical Performance

• On COCO2017, Faster-R-CNN+FPN (ResNet-50) default mAP: 36.4%. With AABO: 38.8% (+2.4% absolute).
• Mask R-CNN R101: 40.3% → 42.3% (+2.0% mAP).
• Generalization holds across model backbones and both one-stage/two-stage detection paradigms.

4. Comparative Analysis of AnchorOPT Variants

Variant (arXiv)	Domain	Mechanistic Anchor Use
ADPO (Zixian, 21 Oct 2025)	Preference Optimization	Reference-policy anchoring, groupwise regularization
Prompt Learning (Li et al., 26 Nov 2025)	Vision-LLMs	Learned anchors + adaptive position matrix
Object Detection (Ma et al., 2020)	Object Detection (FPN, COCO)	Anchor box hyperparameter BO/SMC

Each AnchorOPT instantiation exploits anchoring in contextually specific forms: as teacher reference policies, token-level prompt anchors, or spatial anchor boxes. The unifying mechanism is the stabilization, regularization, or efficient search imparted by anchor-based constructs within the core learning or transfer process.

5. Significance, Limitations, and Future Directions

ADPO demonstrates improved robustness and sample efficiency under severe noise in both contextual bandits and RL. The dynamic-anchor prompt learning approach allows adaptation across datasets and domains without hand-engineered tokens, consistently outperforming static baselines and alternative token arrangements. For object detection, AABO delivers architectural-agnostic mAP lifts by optimizing anchor configurations with efficient resource use via SMC pruning.

Potential drawbacks include increased parameter count (notably $O((N+M)^2)$ for the AnchorOPT position matrix in prompt learning), and two-stage training procedures requiring extra data preprocessing (e.g., for anchor token pretraining or anchor box statistics). A plausible implication is that further efficiency gains may be possible by integrating anchor learning with joint end-to-end optimization and extending to broader foundation models, multi-modal tasks, or hierarchical anchoring strategies.

• "ADPO: Anchored Direct Preference Optimization" (Zixian, 21 Oct 2025)
• "AnchorOPT: Towards Optimizing Dynamic Anchors for Adaptive Prompt Learning" (Li et al., 26 Nov 2025)
• "AABO: Adaptive Anchor Box Optimization for Object Detection via Bayesian Sub-sampling" (Ma et al., 2020)