Self-Predictive Policies in RL

• Self-predictive policies are reinforcement learning strategies where agents explicitly predict aspects of their future performance, internal states, or uncertainty to inform decision making.
• They integrate auxiliary self-supervision, bootstrapping, and action-conditioned updates to refine representations and improve control optimization in partially observed settings.
• These methods have shown practical success in robotics, adaptive control, and high-dimensional planning by addressing challenges like credit assignment, noise robustness, and model generalization.

Self-predictive policies refer to a broad set of reinforcement learning (RL) and control paradigms in which agents are trained to explicitly model, anticipate, or optimize for aspects of their own future performance, internal beliefs, representations, or uncertainty. These approaches unify several strands of research in representation learning, model predictive control, state predictivity, and auxiliary self-supervision in RL. Self-predictive policy frameworks can address challenges including partial observability, credit assignment, noise robustness, adaptability, and generalization, providing powerful tools for developing agents with model-awareness and anticipatory capabilities.

1. Core Principles of Self-Predictive Policies

The central theme in self-predictive policy research is the explicit incorporation of agent-internal forecasts or predictions into policy learning or control optimization. Key aspects include:

• Self-predictive abstraction: A representation is self-predictive if it enables the agent not only to infer rewards and values from the latent space but also to predict its own future latent state under policy-induced or action-conditional transitions (Ni et al., 17 Jan 2024, Khetarpal et al., 4 Jun 2024). This notion extends classical state abstraction to include end-to-end learned representations.
• Model-aware control: In advanced model predictive control (MPC) schemes, controllers optimize not only for nominal performance but also anticipate their own future limitations under uncertainty—propagating both state uncertainty and higher-order sensitivity measures to penalize anticipated suboptimality (Houska et al., 2016).
• Predictive state representations: Predictive state policy networks encode futures in terms of observable quantities (e.g., future measurement distributions) and make control decisions based on these predictive beliefs (Hefny et al., 2018).
• Bootstrapping and auxiliary losses: Self-predictive learning often relies on bootstrapped targets—predicting future encoded state or features based on current representations, sometimes requiring action conditioning and careful regularization to avoid degenerate solutions (Ni et al., 17 Jan 2024, Khetarpal et al., 4 Jun 2024).

2. Theoretical Foundations and Objectives

Multiple frameworks formalize self-predictivity through optimized auxiliary objectives or system-level expansions:

• Self-reflective MPC loss expansion: The stage cost is augmented with a second-order approximation of the expected control loss, capturing the interaction between state estimate variance (forward-propagated by an EKF) and sensitivity matrices from adjoint (backward) propagation. The key penalty has the form

$$\mathcal{L}(x_k, u_k, \Sigma_k, \Omega_{k+1}) = \frac{1}{2} \mathrm{Tr}(\Phi_k \Sigma_k),$$

where $\Phi_k$ is derived from the Riccati-adjoint recursion and $\Sigma_k$ is the state covariance (Houska et al., 2016).

• Self-predictive representation objectives: In RL, given an encoder $\phi(h)$ (of history $h$), the self-predictive property requires that for a transition $h,a,o'$, the predicted next embedding $g_\theta(\phi(h), a) \approx \phi(o')$ (often enforced via an $\ell_2$ or KL loss):

$$J_\ell(\phi, \theta, \overline{\phi}; h, a) = \mathbb{E}_{o' \mid h, a}\left[ \| g_\theta(\phi(h), a) - \overline{\phi}(o') \|^2 \right],$$

with $\overline{\phi}$ a stop-gradient or EMA encoder copy to mitigate representational collapse (Ni et al., 17 Jan 2024).

• Action-conditional self-predictivity: Recent work introduces action-conditional variants such as BYOL-AC, where separate predictors $P_a$ are learned for each action, with the loss

$$\mathbb{E}_{x,a,y} \left[ \| P_a^\top \Phi^\top x - \text{sg}(\Phi^\top y) \|^2 \right],$$

highlighting the need to learn distinctions between action-specific transitions and capturing a richer class of dynamics (Khetarpal et al., 4 Jun 2024).

• Divergence-minimization in policy optimization: Self-imitation learning frames policy improvement as minimizing a divergence (e.g., Jensen-Shannon) between the present behavior and a distribution of previously successful state-action visitations, generating dense internal “shaped” rewards from the agent’s own high-return history (Gangwani et al., 2018).

3. Optimization Techniques and Algorithmic Patterns

Self-predictive policy learning requires specific algorithmic safeguards and architectures:

• Stop-gradient regularization: To prevent the trivial solution (constant or collapsed representations) in bootstrapped embedding losses, target networks are updated with detached parameters or moving averages, ensuring that fixed-point solutions are not degenerate (Ni et al., 17 Jan 2024).
• Two-stage or alternating updates: Methods such as RPSP utilize an initialization phase (e.g., spectral learning to fit predictive state models), followed by end-to-end joint or alternating updates for both the predictive filter and the policy to balance interpretability and learning efficacy (Hefny et al., 2018).
• Ensembling and diversity promotion: Self-predictive, self-imitating approaches can be extended to ensembles via SVPG with a kernel encouraging diversity (i.e., repulsive regularization in the policy parameter space based on divergence between visitation distributions), reducing mode collapse and increasing robustness in exploration (Gangwani et al., 2018).
• Explicit rollout and automatic differentiation: Differentiable predictive control architectures “unroll” the policy within a closed-loop dynamics model, allowing efficient, direct optimization via gradient descent through full trajectory forecasts, including all constraints and penalties (Drgona et al., 2020, Drgoňa et al., 2022).
• Meta-gradient descent for predictive feature selection: Agents can dynamically optimize which future-predicting features they should learn via meta-gradients propagated through the control loss, enabling context-dependent, adaptive construction of predictive representations (Kearney et al., 2022).

4. Empirical Evaluation and Applications

Self-predictive policies have demonstrated effectiveness across a wide variety of domains:

• Model predictive control under uncertainty: Self-reflective MPC achieves lower expected control performance loss and robust closed-loop trajectories, as shown in predator–prey systems with partial observability (Houska et al., 2016).
• Robotics and control in partially observed settings: RPSP networks outperform standard RNNs and finite-memory models on robotic control benchmarks by leveraging explicit predictive state tracking (Hefny et al., 2018).
• Adaptive and transfer learning: Adaptive goal-setting via evolving neural goals enables rapid transfer of predictive models to new tasks, such as changing survival objectives in VizDoom scenarios (Ellefsen et al., 2019).
• Policy generalization in non-stationary environments: Prognosticator algorithms that forecast future performance provide improved regret minimization compared to standard online or recency-based adaptation, especially under gradual, exogenous non-stationarity (e.g., in diabetes management or drifting robotic goals) (Chandak et al., 2020).
• Efficient high-dimensional planning: Dual-policy and self-model approaches boost planning efficiency and stability by using compact distilled networks to simulate one’s own policy in high-dimensional searches such as MCTS, enhancing exploration and reducing computational overhead (Yoo et al., 2023).

5. Theoretical Connections and Unifying Frameworks

Emerging research highlights common mathematical underpinnings across disparate approaches:

• Spectral and value-learning connections: Action-marginalized and action-conditional self-predictive objectives (e.g., BYOL-$\Pi$, BYOL-AC, and BYOL-VAR) correspond, respectively, to capturing the principal directions of the average squared policy-induced transition matrix, averages of squared per-action transitions, and the variance across actions. These link representation learning tightly with the estimation of state-value, Q-value, and advantage functions (Khetarpal et al., 4 Jun 2024).
• Reward function recovery via latent dynamics: If the latent embedding supports both next-state prediction and accurate representation of optimal Q-values, it is possible to reconstruct the reward function via a BeLLMan-residual-like operator:

$$\mathcal{R}_n(z,a) = \mathcal{Q}(z,a) - \gamma \mathbb{E}_{z’ \sim P_n(\cdot|z,a)} [\max_{a’} \mathcal{Q}(z’,a’)],$$

allowing latent models to serve as sufficient statistics for both planning and policy evaluation (Ni et al., 17 Jan 2024).

Objective	Focused Dynamics	Value Correspondence
BYOL‑$\Pi$	Policy-marginal T$^\pi$	State-value V
BYOL‑AC	Per-action T$_a$	Q-value
BYOL‑VAR	Residual/variance	Advantage

This table illustrates how action-conditionality and variance targeting relate distinct self-predictive losses to specific control-relevant value functions.

6. Limitations and Open Challenges

While self-predictive frameworks provide significant benefits, several challenges persist:

• Representational collapse: Without explicit decoupling (via stop-gradient or EMA), self-predictive bootstrapping can drive the encoder to constant solutions, eliminating useful information (Ni et al., 17 Jan 2024).
• Overfitting auxiliary tasks: Aggressive regularization or suboptimal auxiliary task weighting may improve predictive loss at the expense of task performance. Balancing the main RL loss and predictive auxiliary losses is non-trivial (Hefny et al., 2018).
• Approximation validity: For second-order expansions (as in self-reflective MPC), theoretical guarantees depend on small noise/mild nonlinearities; robustness outside this assumption remains an issue (Houska et al., 2016).
• Computational resources: Methods requiring backward and forward recursions (e.g., propagating adjoint states, maintaining ensembles), while efficient relative to naive optimization, may still pose practical burdens for high-dimensional systems or real-time constraints.
• Extensibility to multi-agent and hierarchical RL: While self-predictive/self-model approaches can inform extensions to multi-agent “theory of mind” and temporally abstracted control, more empirical and theoretical work is needed to validate their effectiveness and stability in such contexts (Yoo et al., 2023).

7. Practical Guidelines and Future Directions

The synthesis of empirical and theoretical findings leads to a range of recommendations and research avenues:

• Initialization: For predictive state architectures, leveraging model-based or spectral initializations improves trainability and interpretability (Hefny et al., 2018).
• Auxiliary task formulation: Prefer action-conditional self-predictive objectives (e.g., BYOL-AC) for domains where discriminating action effects is critical; use variance-based objectives for advantage learning or option discovery (Khetarpal et al., 4 Jun 2024).
• Regularization: Adopt stop-gradient/EMA strategies and tune auxiliary weights to ensure stable and non-trivial representations (Ni et al., 17 Jan 2024).
• Algorithm minimalism: Where possible, use minimalist approaches that jointly optimize main RL and self-predictive losses without unnecessary additional networks or multi-step prediction targets (Ni et al., 17 Jan 2024).
• Performance monitoring: Regularly evaluate both main-task returns and diagnostic indicators of representation quality (e.g., rank, variance, prediction error on held-out transitions).
• Transfer and adaptation: Incorporate self-predictive models to facilitate transfer across task variants, particularly when new goals, objectives, or environmental dynamics are encountered (Ellefsen et al., 2019).
• Integration with ensemble and diverse policy portfolios: Where robustness or coverage is required, ensemble self-predictive agents and explicitly promote diversity in internal representations and policies (Gangwani et al., 2018).

Self-predictive policy frameworks thus offer a theoretically grounded and empirically validated foundation for the next generation of adaptive control and reinforcement learning agents, unifying dynamic model-awareness, value-based abstraction, and self-supervised representation learning.