Horizon Generalization in Sequential Tasks

• Horizon generalization is the ability of models, algorithms, or agents to maintain robust performance as task or decision process lengths increase.
• It uses methodologies like hierarchical decomposition, planning invariance, and memory augmentation to overcome the challenges of sequential and long-horizon regimes.
• This concept is crucial in robotics, reinforcement learning, and control, enabling robust extrapolation from simple training tasks to complex, multi-stage real-world scenarios.

Horizon generalization refers to the ability of models, algorithms, or agents to maintain robust performance as the temporal or sequential length (“horizon”) of tasks, policies, or decision processes increases. The phenomenon is critical across robotics, reinforcement learning, planning, sequential recommendation, control, and even theoretical and physical settings. It formalizes and measures the capacity to extrapolate or transfer behavioral competence from short-horizon to long-horizon regimes, encompassing both planning and execution under increased complexity, compounded dependencies, or uncertainty. Horizon generalization is distinct from classical out-of-distribution or task-variant generalization; it specifically interrogates the inductive bias and architectural mechanisms that enable an algorithm trained on low-horizon tasks to operate effectively when the horizon is substantially extended.

1. Definitions and Theoretical Formalizations

Horizon generalization is mathematically framed by how solution quality or policy optimality scales with horizon length. In reinforcement learning, particularly goal-conditioned RL, it asks whether a policy $\pi(a|s,g)$ trained to reach nearby (short-horizon) goals generalizes to distant (long-horizon) goals. The formal criterion is that optimality on the set $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$ implies optimality on all $(s,g)$, i.e., $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$ for all $c>0$, where $\mathcal{E}_{\mathrm{gen}}$ is a value-function gap outside the training ball (Myers et al., 6 Jan 2025).

In temporal user modeling, horizon generalization is operationalized as the ability of the model to predict or recommend correctly interactions or behaviors beyond a temporal cutoff $\tau$, reflecting a strictly held-out “future” (Goel et al., 19 Apr 2026). In control and MPC, it concerns whether a controller tuned for finite (short) horizons yields stability, feasibility, or near-optimality as the horizon grows (or in the infinite-horizon limit) (Nascimento et al., 24 Mar 2025), whereas in robotics and manipulation the focus is on compositionality and skill chaining under increased task decomposition depth (Chen et al., 15 Oct 2025).

Key domains have introduced summary metrics for horizon generalization:

• Success rate $S(H)$: Success probability as a function of the number of stages $H$, decomposed by atomic tasks $S_A(H)$, compositional tasks $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$0, and with perturbations $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$1, $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$2 (Chen et al., 15 Oct 2025).
• Compositional Generalization Gap $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$3: The difference $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$4 as $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$5 increases.
• Temporal recall metrics (e.g., Recall@K): Evaluated on future (post-cutoff) interactions (Goel et al., 19 Apr 2026).
• Horizon-conditioned reachability $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$6: Probability of reaching $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$7 in $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$8 steps, monotonic in $\mathcal{B}_c = \{(s, g): d(s,g)<c\}$9 (Naderian et al., 2020).
• Reach integral: $(s,g)$0 as a function of distance (and thus induced horizon) (Myers et al., 6 Jan 2025).

2. Mechanisms: Hierarchy, Invariance, and Memory

Hierarchical Decomposition

Robust horizon generalization commonly requires explicit temporal or skill hierarchy. Experiments with RoboHiMan present a planner-policy split: a high-level planner ($(s,g)$1) decomposes instructions into subtasks, and a low-level policy ($(s,g)$2) executes them. Success rates collapse for end-to-end (vanilla) models as horizon $(s,g)$3 grows, but explicit hierarchy (even with rule-based planners) increases compositional task success rates by an order of magnitude, though still plateauing at $(s,g)$440% on the hardest settings (Chen et al., 15 Oct 2025). Similarly, LoHo-Manip introduces a decoupled manager (VLM) and executor, with a receding-horizon loop for persistent re-planning and progress-aware memory, achieving significant gains (+15–35 pp) in multi-stage success (Liu et al., 23 Apr 2026).

Planning Invariance

A key theoretical insight is that “planning invariance”—the property that actions chosen towards a distant goal are consistent with those chosen towards chained waypoints—allows generalization from short- to long-range tasks. Specifically, if $(s,g)$5 for some suitable path-relaxing planner, then competence at all sub-goals (within a short-horizon ball) propagates recursively to arbitrarily long horizons (Myers et al., 6 Jan 2025). This invariance is closely linked to path optimality and underlies the robustness of policies based on quasimetric embeddings or cumulative accessibility functions.

Memory and Non-Markovianity

In non-Markovian or phase-dependent domains, e.g., long-horizon manipulation with hidden temporal cues (RuleSafe), standard one-step policies are insufficient. Structured memory representations—VQ-Memory encodes compact, discrete latent tokens summarizing windows of proprioceptive history—enable robust phase tracking across many steps, yielding up to +45% absolute success in challenging, low-observability settings (Honghui et al., 10 Mar 2026). This form of inductive temporal memory is critical as horizon length increases and local context becomes ambiguous.

3. Metrics and Benchmarks for Horizon Generalization

Different research communities have instantiated domain-specific benchmarks for quantifying horizon generalization:

Benchmark/System	Domain	Key Horizon Metric(s)	Evaluation Protocol
RoboHiMan (Chen et al., 15 Oct 2025)	VLA Manipulation	Success rate $(s,g)$6, $(s,g)$7	Decomposition across $(s,g)$8, with perturb.
ExtendaBench (Liang et al., 28 Feb 2025)	Vision-Language Planning	GCR/SR across length bins	Ultra-short to long ($(s,g)$9 to $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$0)
HORIZON (Goel et al., 19 Apr 2026)	User Modeling	Recall@K, MRR@K post-$\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$1	Test on post-cutoff (future) events
RuleSafe (Honghui et al., 10 Mar 2026)	Non-Markov Manipulation	SR, PS per step count	Tasks with $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$2 to $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$3+ phases
DeCoBench (Chen et al., 1 May 2025)	Skill Composition	Task success (%), OOD rate	Zero-shot atomic-to-composite transfer
C-Learning (Naderian et al., 2020)	Goal RL	$\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$4 across $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$5	Evaluate unseen $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$6 at test time

Contextualizing results on these metrics is key: for example, success rates in RoboHiMan’s vanilla (no planner) models are near zero for $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$7, while decoupled hierarchy achieves up to 39.5% under heavy perturbations (Chen et al., 15 Oct 2025). In RuleSafe, VQ-Memory enables up to 45% success for 8-step, phase-dependent safes vs. 0% for memoryless policies (Honghui et al., 10 Mar 2026).

4. Algorithmic and Training Regimes for Generalization

• Curriculum Learning: Structured bootstrapping, starting with short-horizon tasks and progressively increasing horizon, improves generalization to longer tasks and stabilizes RL training (Liang et al., 28 Feb 2025, Kim et al., 4 May 2026). In complex puzzles, curriculum greatly increases long-horizon pass@K success compared to direct RL (Kim et al., 4 May 2026).
• Horizon reduction: Abstraction via macro-actions or explicit subgoal decomposition directly reduces effective horizon length during RL, mitigating credit assignment and exploration challenges, and is empirically shown to produce more robust generalization curves (Kim et al., 4 May 2026).
• Compositional and Modular Planning: Frameworks like DeCo reframe demonstrations as atomic skill libraries and leverage VLM-based parsing for zero-shot composition at inference time, generating large gains on unseen long-horizon tasks even with minimal atomic skill data (Chen et al., 1 May 2025).
• Horizon-Conditioned Networks: C-Learning parameterizes $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$8 for all $\mathcal{E}_{\mathrm{gen}}(\pi;c)=0$9, learning to interpolate across horizons, yielding reliable control over unseen test horizons with a single network instance (Naderian et al., 2020).
• Memory-augmentation: Discrete memory architectures (e.g., VQ-Memory) that can encode long temporal dependencies at minimal compute cost are critical for non-Markovian long-horizon regimes (Honghui et al., 10 Mar 2026).

5. Limitations, Failure Modes, and Open Challenges

Empirical and theoretical work identifies consistent bottlenecks:

• Scalability Ceiling: Despite hierarchy and curriculum, a persistent compositional gap (e.g., $c>0$0–70 pp) remains as horizons increase and perturbations compound (Chen et al., 15 Oct 2025). Data scaling alone is demonstrably insufficient.
• Plan–Policy Coordination: Integrated planner-executor architectures suffer from compounding errors; offline planner accuracy may exceed 65%, yet actual online coupled performance often drops by 30–40 pp (Chen et al., 15 Oct 2025).
• Exploration–Credit Assignment: Atomic-action RL on L3–L4 Sudoku and long-horizon Rush Hour collapses due to the exponential blowup in state-action space and vertically spanned credit-assignment paths (Kim et al., 4 May 2026).
• Memory and Generalization Tradeoffs: Excessively long sequence modeling or fully explicit history grows computationally intractable, requiring careful abstraction (e.g., clustering of memory tokens) for practical gains (Honghui et al., 10 Mar 2026).
• Distribution Shift: Temporal generalization is distinct from classic OOD: strong in-training performance (e.g., Recall@50 $c>0$140%) can degrade by $c>0$230 pp when models are evaluated on post-horizon (future) or OOD user splits (Goel et al., 19 Apr 2026).

6. Future Directions and Methodological Recommendations

Authors consistently propose several methodological fronts for advancing horizon generalization:

• Feedback-rich hierarchical architectures: Integrate closed-loop verification/failure signals to support online replanning and robust dynamic correction (Chen et al., 15 Oct 2025).
• Perturbation-aware abstractions: Develop subtask definitions that are robust to sensor, appearance, or environmental variance (Chen et al., 15 Oct 2025).
• Semantic, content-based representations: In sequential modeling, use semantic or context-grounded representations to bridge the temporal gap more effectively than vanilla sequence modeling (Goel et al., 19 Apr 2026).
• Learned memory and hierarchical VQ-modules: Evolve the VQ-Memory paradigm to multi-modal, hierarchical, or jointly end-to-end training for ultra-long horizons (Honghui et al., 10 Mar 2026).
• Adaptive horizon-aware curriculum and meta-learning: Leverage diverse, combinatorial sequence curricula and meta-learning to foster skill recomposition and flexibility at inference (Chen et al., 15 Oct 2025, Liang et al., 28 Feb 2025).
• Explicit planning invariance via architectural constraints: Enforce quasimetrics, triangle inequalities, or planning-invariant objectives via normalization-style or residual-net modules (Myers et al., 6 Jan 2025).
• Domain-agnostic abstraction–translation decompositions: Separate planning in simplified or abstract MDPs from trajectory execution, using powerful translation architectures to close the domain gap (Tao et al., 2022).

Collectively, horizon generalization research seeks to uncover algorithmic and representational principles—hierarchy, invariance, modularity, memory—that enable robust extrapolation along the temporal dimension, turning short-horizon competence into long-horizon mastery across planning, learning, and control.