[Paper] DFORD: Directional Feedback based Online Ordinal Regression Learning

Source: arXiv - 2512.19550v1

Overview

The paper “DFORD: Directional Feedback based Online Ordinal Regression Learning” tackles a realistic weak‑supervision scenario: instead of receiving the exact ordinal label (e.g., rating 1–5), a learning system only learns whether its prediction lies to the left or right of the true label. The authors design an online algorithm that can learn effectively from this minimal feedback, extend it to nonlinear kernels, and prove a logarithmic regret bound—showing that the method quickly approaches the performance of a fully supervised learner.

Key Contributions

• Directional feedback model for ordinal regression, a weaker supervision signal than full labels.
• DFORD algorithm: an online exploration‑exploitation scheme that updates both the weight vector and the ordered thresholds using only left/right cues.
• Kernelized DFORD with a truncation trick that keeps the model’s memory footprint bounded while still capturing non‑linear relationships.
• Theoretical guarantee: expected regret grows only as (O(\log T)), matching the best possible rates for online learning under full information.
• Empirical validation on synthetic and real‑world datasets, demonstrating performance on par with (and occasionally surpassing) fully supervised baselines.

Methodology

1. Problem Setup – An instance (x_t) arrives, the model predicts an ordinal class using a set of ordered thresholds ({\theta_i}). The learner only receives a binary signal: “prediction is too low” (left) or “prediction is too high” (right).
2. Exploration‑Exploitation – DFORD mixes two actions:
   • Exploration: with a small probability it perturbs the prediction to gather informative feedback.
   • Exploitation: otherwise it updates the model using a stochastic gradient step derived from the directional signal.
3. Threshold Maintenance – Updates are designed so that, in expectation, the thresholds remain ordered (i.e., (\theta_1 \le \theta_2 \le \dots)). This preserves the ordinal structure without explicit projection.
4. Kernel Extension – The algorithm is lifted to a reproducing‑kernel Hilbert space. To avoid the classic “ever‑growing” support‑vector set, the authors apply a truncation trick: older basis functions are dropped once their contribution falls below a threshold, keeping the model size bounded.
5. Regret Analysis – By bounding the variance introduced by exploration and leveraging the convexity of the surrogate loss, the authors prove an expected regret of (\mathcal{O}(\log T)) over (T) rounds.

Results & Findings

Key takeaways

• DFORD’s accuracy is within 0.5 % of the fully supervised oracle on most benchmarks.
• The kernelized version captures non‑linear patterns without exploding memory, thanks to truncation.
• The regret curve empirically follows a logarithmic trend, confirming the theoretical bound.

Practical Implications

• User‑feedback systems (e.g., “thumbs up/down” on a recommendation) can now be leveraged for ordinal tasks like rating prediction without asking users for exact scores.
• Edge and streaming environments benefit from the online nature and bounded memory of the kernel variant, enabling real‑time ordinal predictions on devices with limited resources.
• A/B testing platforms can incorporate DFORD to continuously improve ranking or severity‑scoring models while only collecting cheap binary signals.
• Privacy‑sensitive applications: directional feedback reveals less personal information than exact labels, easing compliance with data‑protection regulations.

Limitations & Future Work

• Assumption of consistent directional feedback – the analysis presumes the feedback is always correct; noisy or adversarial signals could degrade performance.
• Threshold initialization can affect early‑stage convergence; the paper uses heuristic seeds, leaving room for more principled strategies.
• Scalability to very high‑dimensional kernels still hinges on the truncation threshold; adaptive schemes could further tighten memory usage.
• Future research directions suggested include extending DFORD to partial‑order settings, handling multi‑label ordinal problems, and integrating confidence‑weighted exploration to reduce the number of required exploratory steps.

Authors

• Naresh Manwani
• M Elamparithy
• Tanish Taneja

Paper Information

• arXiv ID: 2512.19550v1
• Categories: cs.LG
• Published: December 22, 2025
• PDF: Download PDF