Iterative Reward-Driven Refinement

• Iterative reward-driven refinement is a method that incrementally updates reward functions by incorporating targeted human input to better align agent behaviors with evolving preferences.
• It employs a divide-and-conquer strategy using feature traces and online gradient updates to systematically address representational deficiencies in conventional reward models.
• Empirical evaluations in robotics and simulation demonstrate reduced sample complexity, improved generalization, and enhanced safety through iterative, human-in-the-loop refinements.

Iterative reward-driven refinement is a class of learning and optimization methods that systematically improve agent behaviors or model outputs by repeatedly updating reward functions, policies, or system configurations based on targeted feedback, observed performance, or explicit interventions. In the context of robotics and machine learning—exemplified by the framework in "Feature Expansive Reward Learning: Rethinking Human Input"—the objective is to align agent actions with nuanced, evolving, or under-specified human preferences by decomposing the reward learning process into sequential, data-efficient, and interpretable refinement steps.

1. Divide-and-Conquer Reward Structure and the Iterative Framework

The approach begins by acknowledging the limitations of conventional reward function design, which typically employs a fixed set of hand-engineered features. In these systems, the agent's reward function is parameterized as $r_\theta(\phi(s))$, where $\phi(s)$ denotes a feature vector constructed from the state $s$. If an agent’s policy, trained using such a reward function, yields behavior that elicits corrective human intervention (e.g., kinesthetic correction), and these corrections cannot be accurately modeled by the existing feature set, this signals a representational deficiency.

To address this, the framework implements a divide-and-conquer strategy:

• The agent monitors whether the current reward function sufficiently explains observed human interventions using a confidence score, such as one computed from a Boltzmann-rational observer model.
• Upon detecting inadequacy (e.g., low estimated confidence parameter $\beta$), the agent actively queries for additional, targeted human input to resolve its ambiguity.
• The process is intrinsically iterative: each refinement adds a feature to the representation and updates $\theta$, repeating as necessary until observed human corrections can be explained.

This structure supports efficient, incremental alignment of the reward specification with latent or evolving user preferences, and provides direct mechanisms for error diagnosis and correction within complex, high-dimensional task spaces.

2. Human Input via Feature Traces

A distinguishing contribution of this iterative refinement paradigm is the "feature trace" input mechanism. Unlike standard demonstrations, feature traces are structured partial trajectories specifically targeting the feature missing from the agent's reward representation. For a feature $\phi$ exhibiting unintended agent behavior, the human demonstrator guides the agent through a sequence $(s_0, s_1, \dots, s_n)$ such that $\phi(s_i) \geq \phi(s_j)$ for all $i < j$, enforcing a monotonic decrease. Each trajectory serves as direct "instruction" to the agent about the semantic meaning of the missing feature.

This process yields a collection of state pairs with strong ordinal constraints, which forms a dataset $\mathcal{D}$ of pairwise comparisons annotated as $y = 1$ if $s \succ s'$ (i.e., $s$ should be ranked higher), $y=0$ otherwise, and $y=0.5$ for cross-trace ambiguity at endpoints. The agent uses these examples to quickly fit a neural network-based feature function $\phi_\psi(s)$ (mapped to $[0,1]$), explicitly addressing the missing aspect in the reward function.

3. Sample Complexity and Generalization Benefits

Compared to traditional deep inverse reinforcement learning (deep IRL), which infers $r(s)$ over the full state space by implicitly solving for all reward relevant distinctions from demonstrations, the feature trace method localizes the learning burden:

• Each iteration focuses on a single, well-defined aspect, learning a feature from highly informative monotonic data.
• The cross-entropy loss for learning $\phi_\psi$ is defined as:

$$L(\psi) = -\sum_{(s,s', y) \in \mathcal{D}} \left[ y \log P(s \succ s') + (1-y) \log (1 - P(s \succ s')) \right],$$

with $$P(s \succ s') = \frac{\exp(\phi(s))}{\exp(\phi(s)) + \exp(\phi(s'))}$$.

• The resulting feature function generalizes better to unseen states; its structure is forced to match human-defined orderings even outside the support of the provided traces, unlike IRL reward functions prone to overfitting poorly informative demonstrations.

Empirically, this method achieves significantly lower normalized MSE between predicted and ground-truth features with fewer feature traces than required by deep IRL, as shown in results from both physical robot experiments and user studies in simulation.

4. Iterative Reward Weight Updates

Once a new feature $\phi_\psi$ is learned, it is appended to the current feature representation, and the reward model is updated:

• The agent maps the original trajectory $\tau$ and the corrected (human-induced) trajectory $\tau_{H}$ to their respective feature exposure sums, computing the difference.
• The reward weights are updated online via:

$$\theta \leftarrow \theta - \alpha \left[ \sum_{s \in \tau_H} \phi(s) - \sum_{s \in \tau} \phi(s) \right]$$

with learning rate $\alpha$.

• This update closely mirrors established reward learning from correction paradigms, utilizing the explicit corrections (now represented in the expanded feature space) to efficiently align the reward model to human intent.

If confidence in the newly augmented reward remains low (estimated using a Bayesian update of confidence parameter $\beta$ with observed human actions under $P(a_H|\theta, \beta)$), further feature refinement can be triggered, yielding an iterative, closed-loop human-in-the-loop refinement protocol.

5. Experimental Validation and Quantitative Outcomes

The effectiveness of this approach is validated via two primary experimental setups:

• Physical 7DOF Robot Manipulator: The method is tested on safety-critical tasks, such as avoiding carrying a cup over a laptop. Initial learning with only hand-crafted features fails to account for all risks; upon detection, the system queries for feature traces, learns new features, and repeatedly refines the reward, yielding reward landscapes that closely match ground-truth preferences and demonstrate a reduction in high-risk behaviors (as reflected in lower normalized MSE metrics and improved qualitative reward visualization).
• User Studies in Simulation: Non-expert users successfully provide feature traces for abstract constraints (e.g., proxemics, table boundaries), resulting in feature learning with normalized MSE close to expert-provided labels. Subjective feedback from participants indicates the trace-based procedure is intuitive and enables effective teaching. Incorporation of these learned features in reward functions improves planning outcomes over both random and deep IRL baselines, as quantified by average test-time reward and behavioral matching.

The reduction in sample complexity, improvement in generalization, and user paper confirmation of teaching efficacy collectively validate the iterative reward-driven refinement paradigm.

6. Mathematical and Deployment Considerations

Critical mathematical machinery for the method includes:

• Softmax preference modeling for state comparisons.
• Cross-entropy objective over trace-induced pairwise data.
• Online gradient-based reward weight updates.
• Bayesian estimation of reward function uncertainty (with confidence parameter $\beta$, triggering trace queries).
• Structured data collection and update cycles guided by intervention-triggered queries.

From a systems perspective:

• The approach introduces negligible overhead to standard kinesthetic correction or demonstration-driven learning pipelines, but provides a direct pathway to identify and fill representation gaps.
• Each iteration incrementally grows the feature space in interpretable directions justified by human trace input, maintaining an interpretable reward model structure.
• The methodology is amenable to real-world robotics, with demonstrated support for physical and simulated agents, and generalizes to broader human-in-the-loop RL scenarios, including recommendation systems and collaborative human-robot settings.

7. Implications, Generalization, and Broader Applications

The outlined iterative reward-driven refinement scheme exemplifies a practical realization of sample-efficient, generalizable, and interpretable reward learning:

• Isolating and refining features one at a time not only reduces human effort and required data but also improves scalability and enables the system to robustly adapt to evolving human preferences.
• The technique supports continual learning and online adaptation—key for long-horizon, safety-critical, and changing environments.
• This structured approach to reward learning is extensible to any setting where user preferences are complex, changing, or only partially captured by initial feature design.

The general methodology, as formalized in this work, forms a foundational building block for robust, scalable reward inference in modern interactive agent systems (Bobu et al., 2020).