Preview-Based Policy in Control & RL

• Preview-based policy is a decision framework that leverages forecasted future data—such as disturbances, predicted states, or model errors—to inform current control actions.
• It integrates techniques across reinforcement learning, optimal control, and robotics by employing methods like trajectory imagination, disturbance preview, and error-informed fixed-point computations.
• Applications include risk-aware planning in autonomous driving, robust control in safety-critical systems, and video-based prediction for enhanced robotic manipulation.

A preview-based policy is any decision process or control law that utilizes predictions or previewed information about future exogenous signals, disturbances, or system states to select the current action. This paradigm appears across reinforcement learning, optimal control, and robotics, leveraging either learned or model-based forecasts to anticipate outcomes, enhance safety, or optimize performance. Formulations range from explicit trajectory imagination in RL, through disturbance preview in safety-critical control, to exploitation of over-approximation errors as preview signals for nonlinear systems.

1. Mathematical Formulation of Preview-Based Policies

The defining property of a preview-based policy is its dependence not only on the current state but also on future or predicted data. Abstractly, a preview-based policy has the form

$\pi(a_t \mid s_t, \mathcal{P}_t)$

where $s_t$ is the current system state and $\mathcal{P}_t$ is a set of previewed variables—such as future disturbances $d_{t:t+p}$, predicted states $s_{t+1:t+H}$, or model errors $e(x_t, a_t)$—available at time $t$.

Key instantiations include:

• Imagination-based RL: $\mathcal{P}_t$ encodes a finite or stochastic set of multi-step predicted future latent states generated by a learned or analytical dynamics model (Liu et al., 31 Jul 2024, Hu et al., 19 Dec 2024).
• Disturbance-preview in safety control: $\mathcal{P}_t$ provides a finite-horizon preview of future exogenous disturbances, which augments the state for safety analysis (Liu et al., 2023).
• Error-informed policies for nonlinear control: $\mathcal{P}_t$ is the over-approximation error, which can be computed once $a_t$ is hypothesized, allowing policies of the form $\pi(x, e)$ to be concretized via fixed-point formulations (Aspeel et al., 5 Nov 2025).
• Sensor-driven preview in planning: For example, sensor modules predict occupancy or collision likelihoods for future positions or time steps, and provide these as input to the planning algorithm (Mazouchi et al., 2021).

These formulations require that the preview information is either directly measured (e.g., by sensors), forecasted via an explicit model, or simulated via latent dynamics.

2. Preview-Based Policies in Model-Based Reinforcement Learning

Imagination-based or preview-based RL methods integrate a learned dynamics model into the policy selection loop, enabling agents to roll out candidate action sequences and evaluate imagined outcomes before acting.

ProSpec: Plan Ahead, then Execute (Liu et al., 31 Jul 2024)

Let $(S, A, P, R, \gamma)$ define the MDP, with continuous state and action spaces. The ProSpec framework intervenes as follows:

1. Encode current state: $z_t = f(s_t)$ via a learned encoder.
2. Imagine $k$ action rollouts: For each $i=1...k$, sample a random action sequence $\tilde{a}^{i}_{t:t+H-1}$ of horizon $H$, and generate the imagined trajectory

$$\hat{z}^{i}_{t} = z_t~,~\hat{z}^{i}_{t+h+1} = h_\theta(\tilde{a}^{i}_{t+h}, \hat{z}^{i}_{t+h}),$$

where $h_\theta$ is an invertible (RealNVP-based) latent dynamics model.

1. Score rollouts: Compute for each perspective

$$CQ^i = \sum_{h=0}^{H-1} \gamma^{h} Q_\phi(\hat{z}^{i}_{t+h}, \tilde{a}^{i}_{t+h}),$$

using the current Q-function $Q_\phi$.

1. Select and execute action: Choose $\tilde{a}^{i^*}_{t}$ of the highest-scoring trajectory $i^* = \arg\max_i CQ^i$.

A cycle-consistency constraint is enforced on the dynamics model by inverting the imagined trajectory to recover the initial latent $z_t$, ensuring reversibility and discouraging planning into irreversible or low-density regions.

The preview-based policy is thus

$$a^*_t = \tilde{a}^{i^*}_t~,~i^* = \arg\max_{i} \text{Score}(\tilde{a}^{i}_{t:t+H-1}).$$

Empirically on DMControl (100K frames), ProSpec achieves a median score of 807.5 ($+8.32\%$ over PlayVirtual; $+9.64\%$ over SPR), and ranks first on five of six test tasks.

3. Preview in Safety-Critical and Robust Control

Preview information is central in designing robust controllers and invariant sets that guarantee safety under uncertainty.

Disturbance Preview and Safety Regret (Liu et al., 2023)

Given a controlled system

$$x_{t+1} = f(x_t, u_t, d_t),~~d_t \in D,~x_t \in \mathbb{R}^n,~u_t \in \mathbb{R}^m,$$

a $p$-step preview grants access to $(d_t, ..., d_{t+p-1})$ at each $t$. Augmenting the state with previewed disturbances yields an augmented system $\Sigma_p$ whose maximal robust controlled-invariant set $C_{\max, p}$ (projected onto $x$) is $Z_p$. The limit $p \to \infty$ yields $Z_\infty$.

Safety regret is quantified by the Hausdorff gap:

$\Delta_p := d_H(Z_\infty, Z_p).$

For linear systems with appropriate stabilizability, the main result is that

$\Delta_p \le C e^{-\alpha p}.$

Thus, the marginal gain in safety decays geometrically with preview horizon. This guides systematic selection of preview horizon $p$ to achieve tolerated safety-regret $\varepsilon$:

$$p \ge \frac{1}{\alpha} \log \left( \frac{C}{\varepsilon} \right).$$

Practical computation of $Z_p$, $Z_\infty$, and $\Delta_p$ exploits polytopic approximations and backward reachability, with algorithms to handle both controllable and general cases.

4. Nonlinear Control with Error Preview

In nonlinear and over-approximated systems, preview-based (informed) policies utilize known over-approximation errors to reduce conservatism.

Exploiting Over-Approximation Errors (Aspeel et al., 5 Nov 2025)

For nonlinear dynamics $x_{t+1} = f(x_t, u_t)$, consider an approximate model $\hat{f}(x_t, u_t)$ with error $e(x_t, u_t) = f(x_t, u_t) - \hat{f}(x_t, u_t)$.

• Uninformed policy: $u = \pi(x)$, robust to all $e \in E$.
• Preview-based (informed) policy: $u = \hat{\pi}(x, e)$, responsive to the exact $e$ at $t$.

At runtime, one seeks $u = \hat\pi(x, e(x, u))$, i.e., a fixed-point of an operator $\mathcal{F}_x(u)$. Existence is guaranteed by Brouwer's theorem under compactness and continuity.

For input-affine systems, the fixed-point equation is affine in $u$, solved by inversion or LP. For general nonlinear systems, Banach iteration ensures convergence under a contraction mapping. Empirical case studies show that preview-based policies admit greater terminal states and improved control performance relative to robust, uninformed policies.

5. Preview for Risk-Aware Planning and Q-Learning

Preview-based policies in planning and RL often incorporate risk assessments derived from previewed environment or disturbance information, yielding more robust or risk-averse behavior.

Risk-Averse Preview-Based Q-Learning (Mazouchi et al., 2021)

Applied to autonomous driving, the preview-based planner models the road ahead as a finite-state, nonstationary MDP with stochastic cell occupancy and risk labels predicted by sensor fusion. The risk assessment unit leverages:

• Probabilistic motion predictors for other agents.
• Stochastic reachability for collision likelihoods.
• Mapping of risk profiles to reward distributions, penalizing high-variance (unsafe) transitions.

The Q-function to be learned accommodates a risk-averse Bellman equation:

$$Q^*(s, a) = g_k(s,a) + \gamma \frac{1}{\alpha} \log \mathbb{E}_{s'|s,a}\big[\exp(\alpha \min_{a'} Q^*(s', a')) \big],$$

where $g_k(s,a)$ is the certainty-equivalent stage cost from previewed risk, and $\alpha > 0$ is the risk-aversion parameter.

The preview-based policy is obtained by solving a sampled, convex Bellman-inequality program built on imagined (simulated via preview) transitions and running the optimal policy from the resultant Q-function. Hybrid automata and feasibility checks ensure that environment changes leading to infeasibility trigger fast replanning.

Empirically, risk-averse preview-based Q-learning achieves $\sim 50\%$ reduction in lateral variance compared to risk-neutral policies in highway scenarios.

6. Video-Based Preview Policies in Robot Control

Preview-based policies also include those that employ predicted future perceptual embeddings in decision making.

Video Prediction Policy (VPP) (Hu et al., 19 Dec 2024)

VPP employs a pre-trained video diffusion model (VDM) to generate a set of rough predictive embeddings $\{z_{t+1}, ..., z_{t+K}\}$ for future time steps, conditioned on current observation $s_t$ and language instruction $l$.

The action policy $\pi(a_t \mid z_t, z_{t+1:t+K}, l)$ utilizes these future embeddings, aggregated via a Video Former module, to infer actions via a diffusion-based inverse-dynamics head.

Empirical results indicate substantial gains for preview-based policies: VPP achieves a 31.6% increase in dexterous manipulation success rates and 28.1% longer long-horizon skill chains compared to single-frame or contrastive-encoder baselines.

Ablation studies confirm that predicted future visual features capture multi-step dynamics inaccessible to purely static encoders.

7. Computational Considerations and Design Tradeoffs

Preview-based policies universally require additional computational resources to perform prediction, simulation, or fixed-point computation using the preview data. For example, ProSpec incurs the computational cost of $k$ rollout evaluations per decision step (Liu et al., 31 Jul 2024), and safety preview algorithms entail polytope or LMI operations that scale with state dimension but not preview horizon (Liu et al., 2023).

Tradeoffs include:

• Preview horizon: Longer preview improves performance but displays diminishing returns due to geometric decay of "preview regret" (Liu et al., 2023).
• Modeling Error: Policies exploiting exact error preview reduce conservatism but depend on accurate over-approximation and tractable error evaluation (Aspeel et al., 5 Nov 2025).
• Robustness to Model or Sensor Error: Risk assessment units or hybrid automata can mitigate deviations between preview and realized outcomes (Mazouchi et al., 2021).

A plausible implication is that preview-based architectures will become increasingly tractable as hardware and modeling advances reduce the marginal cost of additional preview, thereby shifting the primary challenge to algorithmic design for effective preview exploitation and data efficiency.

---

In sum, preview-based policy frameworks leverage foresight—whether from model-based imagination, exogenous disturbance previews, or perceptual predictions—to improve planning, safety, and sample efficiency in complex, uncertain, or multi-step environments. They have demonstrated substantial empirical benefits across RL, safety-critical control, and robotics, with ongoing research targeting improved computational performance, broader generalization, and seamless integration with risk and safety guarantees.