Transfer-Weighted Auxiliary Rewards in RL

• Transfer-weighted auxiliary reward construction is a family of methods that synthesizes and adapts reward signals to guide exploration and enhance knowledge transfer in RL.
• It employs diverse methodologies such as centralized agents, bi-level optimization, and teacher–student frameworks to modulate auxiliary signals and improve sample efficiency.
• These strategies mitigate negative transfer and facilitate robust learning across multi-task, continual, and multimodal reinforcement learning environments.

Transfer-weighted auxiliary reward construction is a family of methods for synthesizing reward signals in reinforcement learning (RL) by learning, adapting, or selecting auxiliary rewards and data in a manner that optimizes knowledge transfer and task performance. Transfer weights modulate the contribution of distinct sources—tasks, heuristics, data modalities—to an agent’s reward or its learning process. This concept appears across multi-task RL frameworks, teacher–student architectures, meta-learning for reward shaping, and visual-language reward alignment, each tailored to propagate useful signal and improve sample efficiency under sparse or misspecified environments.

1. Core Principles of Transfer-Weighted Auxiliary Reward Construction

Transfer-weighted auxiliary reward construction aims to shape agent learning by systematically controlling:

• The source, selection, or weighting of auxiliary rewards—signals not derived from the environment’s original objective but intended to guide exploration or accelerate convergence.
• The transfer of knowledge (e.g., skills, representations, reward structures) accumulated in one context to another, often through learned, adaptive, or selection-based weights.
• The avoidance of negative transfer or reward misalignment by prioritizing beneficial auxiliary signals and suppressing harmful or redundant ones.

Mathematically, auxiliary rewards are typically integrated as

$$r_{\mathrm{total}}(s,a) = r_{\mathrm{env}}(s,a) + \sum_{i} w_i r^{\mathrm{aux}}_i(s,a)$$

where $w_i$ (transfer weights) are learned, adapted, or selected to maximize long-term return in the target environment.

2. Representative Methodologies

Centralized Reward Agent for Multi-Task RL

The CenRA (Centralized Reward Agent) framework organizes $N$ distributed policy agents—one per task—sharing experience via a single CRA. CenRA employs a two-stage knowledge transfer process:

1. Distillation: The CRA samples from a union of all agents’ replay buffers using a convex mixture of similarity- and performance-based transfer weights:
   • Similarity weight: Computed from encoder hidden-state proximity,

   $$w_i^{\mathrm{sim}} = \frac{\exp(1/s_i)}{\sum_k \exp(1/s_k)}$$

• Performance weight: Based on the tail average episode return,

  $$w_i^{\mathrm{per}} = \frac{\exp(1/R_i^{\mathrm{tail}})}{\sum_k \exp(1/R_k^{\mathrm{tail}})}$$

• Final sampling weight: $$w_i = \alpha w_i^{\mathrm{sim}} + (1-\alpha)w_i^{\mathrm{per}}$$

1. Distribution: The CRA outputs knowledge rewards $$r^{\mathrm{knw}} \sim \pi^{\mathrm{rwd}}(\cdot|s,a)$$, which augment each agent’s sparse environmental reward. This approach enables robust knowledge sharing and improves convergence in sparse-reward domains (Ma et al., 2024).

Bi-level Behavior Alignment

A bi-level optimization scheme assigns transfer weights $\phi \in \mathbb{R}^k$ to designer-specified reward heuristics:

1. Inner loop: Agent policy $\theta^*(\phi)$ is learned via standard RL (e.g., REINFORCE, PPO) under the shaped reward $$r_\phi(s,a) = r_{\mathrm{env}}(s,a) + \phi^\top h(s,a)$$.
2. Outer loop: $w_i$0 is updated to maximize true environment return,

$w_i$1

with implicit-gradient computations. This results in $w_i$2 that reliably enhances, suppresses, or ignores heuristics—as appropriate—enabling safe task transfer and correction of inner-loop RL suboptimality (Gupta et al., 2023).

Teacher–Student Weight Adaptation (Reward Training Wheels)

The RTW framework trains a teacher policy to set vector-valued transfer weights $w_i$3 on auxiliary components at each training step:

• Student reward at time $w_i$4: $w_i$5
• Teacher update: Maximizes cumulative student primary-reward performance via policy gradient in a higher-level MDP, with teacher outputs $w_i$6. RTW discovers adaptive schedules, forming a curriculum across task phases and leading to improved training efficiency, generalization, and robustness compared to fixed-weight baselines (Wang et al., 19 Mar 2025).

Visual Reward Models with Transfer-Weighted Data fusion

RoVRM exploits transfer-weighted combination of textual and visual auxiliary preferences. Key steps include:

• Data selection: Optimal-transport-driven weighting of preference data for transferability, $w_i$7 (from the OT plan $w_i$8).
• Progressive reward construction: Final reward forms a transfer-weighted sum,

$w_i$9

with $N$0. This leverages both rich auxiliary signal and task-specific adaptation (Wang et al., 2024).

3. Transfer Weight Computation Mechanisms

Transfer weights may be computed via:

• Task similarity: As in CenRA, hidden-state cosine similarity among tasks informs the selection of underrepresented or similar tasks for effective knowledge distillation.
• Task or data performance: Empirical reward statistics guide sampling to emphasize struggling or underperforming tasks.
• Gradient-based meta-learning: Bi-level optimization or outer-loop policy gradients, as in behavior alignment and RTW, adapt weights to directly maximize end-task performance.
• Optimal transport matching: In RoVRM, OT across gradient feature distributions identifies text data most likely to transfer to visual preference alignment.

All approaches utilize either normalized softmax or convex-combination schemes, occasionally with regularization (e.g., $N$1, simplex constraints) to ensure stability and interpretable weight schedules.

4. Algorithmic Frameworks

The following table summarizes major transfer-weighted auxiliary reward paradigms:

Framework	Transfer Weight Source	Mechanism/Update
CenRA (Ma et al., 2024)	Task hidden states, returns	On-the-fly convex mixture, softmax sampling
Bi-Level (Gupta et al., 2023)	Heuristic features	Outer-loop gradient meta-optimization
RTW (Wang et al., 19 Mar 2025)	Teacher policy over aux weights	REINFORCE policy-gradient, curriculum
RoVRM (Wang et al., 2024)	OT-matched textual/visual data	Sinkhorn OT row sums, weight-fused loss

In all cases, transfer-weighted rewards modulate the sampling, shaping, or aggregation of auxiliary signals with the aim of improving subsequent learning dynamics.

5. Empirical Outcomes and Theoretical Properties

Across benchmarks:

• Sample efficiency: Transfer-weighted schemes yielded up to 4× speedups or doubled final returns over unshaped or fixed-reward baselines in multi-task and behavior alignment tasks (Ma et al., 2024, Gupta et al., 2023, Wang et al., 19 Mar 2025).
• Mitigation of negative transfer: When auxiliary signals were misaligned, adaptive or transfer-weighted approaches suppressed their influence, matching or surpassing naïve baselines (Gupta et al., 2023, Wang et al., 19 Mar 2025).
• Transfer generalization: Learned weights $N$2 or $N$3 generalized across new tasks, reducing the data and iterations required for adaptation by 2× or more (Gupta et al., 2023, Wang et al., 19 Mar 2025, Wang et al., 2024).
• Effectiveness in vision-language reward modeling: RoVRM’s transfer-weighted auxiliary strategy consistently outperformed direct ranking-based reward learning, both in preference-alignment and visual-linguistic tasks (Wang et al., 2024).

On theoretical grounds, standard off-policy actor–critic convergence criteria apply when using bounded learning rates and stabilized sampling. However, when learned bonuses are not potential-based, classical reward shaping invariance (Ng et al., 1999) does not generally guarantee optimal policy preservation—the methods rely on empirically observed stability and performance gains (Ma et al., 2024).

6. Notable Applications, Limitations, and Directions

Transfer-weighted auxiliary reward construction is well-suited for:

• Multi-task and continual reinforcement learning with varying degrees of task relatedness
• Robotics tasks requiring adaptive curriculum and reward shaping
• Alignment of large language/vision models via multimodal or preference datasets with limited ground-truth

Current limitations include the lack of formal convergence proofs in non-stationary or heavily function-approximated settings, interpretability of weight evolution, and sensitivity to the choice or quality of auxiliary signals. Future work is anticipated to extend transfer-weighted principles to broader settings, incorporating advanced task-similarity metrics, hierarchical architectures, and increased interpretability of transfer dynamics (Ma et al., 2024, Gupta et al., 2023, Wang et al., 19 Mar 2025, Wang et al., 2024).