CaT-RL: Caution-Aware Transfer in RL

• The paper introduces CaT-RL, a framework that transfers risk-neutral policies into risk-aware ones by leveraging generalized caution functions on occupancy measures.
• It employs a one-shot policy construction method that evaluates source policies with a combined reward and caution penalty, avoiding additional retraining in the target domain.
• Empirical validations show up to 80% reduction in unsafe traversals in gridworld and continuous tasks, emphasizing its utility in safety-critical applications.

“CaT-RL” is a precise term used for “Caution-Aware Transfer in Reinforcement Learning via Distributional Risk” (Chehade et al., 16 Aug 2024). It refers to a theoretical and algorithmic framework for transfer learning in reinforcement learning (RL) that explicitly addresses safety by optimizing a general risk notion—termed “caution”—drawn from the occupancy measure of state–action pairs, during the policy transfer process. Unlike conventional transfer RL that narrowly focuses on mean–variance risk metrics, CaT-RL generalizes risk to encompass diverse forms, allowing one-shot construction of risk-aware policies for unseen tasks based on distributions of risk encountered in the test environment.

1. Caution-Aware Transfer RL: Definition and Principles

CaT-RL is specifically designed for the transfer of risk-neutral policies learned on source tasks to new target tasks involving novel risk profiles. The framework evaluates each source policy’s behavior in the target environment and constructs a new target policy by balancing the expected return and a caution (risk) penalty. Formally, given a set of source policies $\{\pi_j^*\}$ trained on MDPs $\{M_j\}$, the target policy $\pi_i$ for a new task $M_i$ is obtained by optimizing

$$W_i^j(s,b) := Q_i^{\pi_j}(s, b) - c \cdot \rho_i(d^{\pi_j})$$

where $Q_i^{\pi_j}(s, b)$ is the action–value under source policy $j$ evaluated in target task $i$, $d^{\pi_j}$ is the state–action occupancy measure, $\rho_i$ is a generalized risk (caution) function, and $c \ge 0$ sets the reward-risk tradeoff. The action $a$ selected in each state $s$ is

$a = \underset{b}{\arg\max}\;\max_{j} W_i^j(s,b).$

This approach does not require additional training in the target domain; risk-sensitive behavior is “injected” post-hoc by making use of distributional information gathered from the occupancy measure in the new environment.

2. Generalized Notion of Risk (Caution)

The “caution” function $\rho(d)$ in CaT-RL generalizes beyond traditional mean–variance risk consideration. It can be any mapping from the occupancy measure of a given policy to a real number representing risk—for example:

• Barrier risk: $\rho(d) = -\log(-d(\overline{S}) + \delta)$ (where $d(\overline{S})$ is the occupancy measure over a set of dangerous states and $\delta > 0$ a smoothing constant),
• Variance risk: $$\rho(d) = \operatorname{Var}(r(s,a,s'); d) = \mathbb{E}^d[(r(s,a,s') - \mathbb{E}^d[r(s,a,s')])^2]$$,
• Occupancy divergence: $\rho(d) = KL(d \parallel \bar{d})$ for some reference occupancy $\bar{d}$.

This allows the framework to represent not only statistical risk (variance) but also barrier constraints or behavioral divergence from expert patterns, thus enabling flexible, context-specific safety considerations in policy deployment.

3. Construction of Risk-Aware Target Policies

Source policies $\pi_j^*$ are evaluated in the target task $M_i$ to produce both $Q_i^{\pi_j^*}$ and $d^{\pi_j^*}$. For each state $s$, all candidate actions $b$ and all source policies are considered. The framework constructs the target policy $\pi_i$ using the rule: $$\pi_i(a|s) = \begin{cases} 1 & \text{if } a = \underset{b}{\arg\max}\;\max_{j}\; [Q_i^{\pi_j}(s,b) - c \cdot \rho_i(d^{\pi_j})] \ 0 & \text{otherwise.} \end{cases}$$ This “one-shot” construction enables rapid transfer to the target task by maximizing $Q$ penalized according to the risk profile given by $\rho$. The policy thus delivered naturally avoids dangerous or highly uncertain states, even if such risks were not encountered or modeled in the original training phases.

4. Theoretical Suboptimality Bounds

CaT-RL provides explicit performance guarantees. Let

$$\tilde{Q}_i^{\pi_j^*}(s,a) = Q_i^{\pi_j^*}(s,a) - c \cdot \rho_i(d^{\pi_j^*})$$

then, for the caution-aware policy $\pi_i$ computed as above, Theorem 1 yields

$$|\tilde{Q}_i^{\pi_i^*}(s,a) - \tilde{Q}_i^{\pi_i}(s,a)| \leq \min_j \left( \frac{2}{1-\gamma} \|r_i - r_j\|_\infty + (4L + K)c \right)$$

with $\gamma$ the discount factor, $L$ the Lipschitz constant of $\rho$, $K$ an upper bound for $|\rho(d)|$, and $\|r_i - r_j\|_\infty$ the maximal reward mismatch between tasks. This bound disentangles the impact of task similarity (first term) from the impact of risk penalty and the caution function’s regularity (second term). It provides rigorous assurances regarding the gap in performance between the optimal risk-aware policy and the constructed CaT-RL policy.

5. Empirical Validation Across RL Domains

CaT-RL was validated in both discrete (gridworld) and continuous (Reacher) environments. In gridworld settings, it successfully transferred policies to tasks with new danger zones, outperforming mean–variance baselines with up to 80% reduction in unsafe traversals. In continuous domains, successor features were employed for source policy evaluation, and CaT-RL produced policies with lower failure rates (i.e., fewer entries into dangerous regions) despite minor decreases in task reward. These results highlight that the occupancy-based risk consideration can robustly handle varying “risk shapes” in new environments.

6. Practical Applications and Real-World Deployment

CaT-RL is especially suited to scenarios where rapid transfer, minimum downtime, and constraint satisfaction are critical. Its one-shot policy construction leverages existing, risk-neutral source policies and applies caution dynamically, making it ideal for safety-critical robotics, autonomous vehicles, and adaptive resource management. Since computational overhead is minimal—policy construction involves only an evaluation sweep—it supports data-efficient adaptation in settings with restricted computational resources and/or limited retraining opportunities.

7. Significance and Future Directions

CaT-RL advances the state-of-the-art in transfer RL by decomposing risk and reward directly in the decision rule via occupancy measures—a departure from mean–variance risk metrics. It enables flexible, theoretically sound, and empirically validated transfer to unseen tasks with new risk profiles without need for retraining. This represents a substantial step toward robust, real-world deployment of RL agents, especially where safety and efficiency must be co-optimized. Future directions may explore further generalizations of $\rho(d)$, integration with online uncertainty estimation, and hierarchical or multi-level risk-aware transfer strategies.