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Horizon Reduction as Information Loss in Offline Reinforcement Learning

Uday Kumar Nidadala, Venkata Bhumika Guthi

TL;DR

The paper addresses the fundamental question of when horizon reduction in offline reinforcement learning preserves the information needed to identify optimal policies. By formalizing horizon reduction as learning from fixed-length trajectory segments, the authors prove that, under this paradigm, optimal and suboptimal policies can become statistically indistinguishable even with infinite data and perfect approximation. They construct three minimal counterexamples—prefix indistinguishability, short-segment optimality violation, and offline support/representation aliasing—to demonstrate intrinsic information-loss mechanisms. They introduce the notion of $H$-sufficiency to characterize safe horizon reduction and outline necessary conditions (identifiability, objective-consistency, and dataset/representation sufficiency) along with practical implications for design, evaluation, and principled use of horizon reduction in offline RL.

Abstract

Horizon reduction is a common design strategy in offline reinforcement learning (RL), used to mitigate long-horizon credit assignment, improve stability, and enable scalable learning through truncated rollouts, windowed training, or hierarchical decomposition (Levine et al., 2020; Prudencio et al., 2023; Park et al., 2025). Despite recent empirical evidence that horizon reduction can improve scaling on challenging offline RL benchmarks, its theoretical implications remain underdeveloped (Park et al., 2025). In this paper, we show that horizon reduction can induce fundamental and irrecoverable information loss in offline RL. We formalize horizon reduction as learning from fixed-length trajectory segments and prove that, under this paradigm and any learning interface restricted to fixed-length trajectory segments, optimal policies may be statistically indistinguishable from suboptimal ones even with infinite data and perfect function approximation. Through a set of minimal counterexample Markov decision processes (MDPs), we identify three distinct structural failure modes: (i) prefix indistinguishability leading to identifiability failure, (ii) objective misspecification induced by truncated returns, and (iii) offline dataset support and representation aliasing. Our results establish necessary conditions under which horizon reduction can be safe and highlight intrinsic limitations that cannot be overcome by algorithmic improvements alone, complementing algorithmic work on conservative objectives and distribution shift that addresses a different axis of offline RL difficulty (Fujimoto et al., 2019; Kumar et al., 2020; Gulcehre et al., 2020).

Horizon Reduction as Information Loss in Offline Reinforcement Learning

TL;DR

The paper addresses the fundamental question of when horizon reduction in offline reinforcement learning preserves the information needed to identify optimal policies. By formalizing horizon reduction as learning from fixed-length trajectory segments, the authors prove that, under this paradigm, optimal and suboptimal policies can become statistically indistinguishable even with infinite data and perfect approximation. They construct three minimal counterexamples—prefix indistinguishability, short-segment optimality violation, and offline support/representation aliasing—to demonstrate intrinsic information-loss mechanisms. They introduce the notion of -sufficiency to characterize safe horizon reduction and outline necessary conditions (identifiability, objective-consistency, and dataset/representation sufficiency) along with practical implications for design, evaluation, and principled use of horizon reduction in offline RL.

Abstract

Horizon reduction is a common design strategy in offline reinforcement learning (RL), used to mitigate long-horizon credit assignment, improve stability, and enable scalable learning through truncated rollouts, windowed training, or hierarchical decomposition (Levine et al., 2020; Prudencio et al., 2023; Park et al., 2025). Despite recent empirical evidence that horizon reduction can improve scaling on challenging offline RL benchmarks, its theoretical implications remain underdeveloped (Park et al., 2025). In this paper, we show that horizon reduction can induce fundamental and irrecoverable information loss in offline RL. We formalize horizon reduction as learning from fixed-length trajectory segments and prove that, under this paradigm and any learning interface restricted to fixed-length trajectory segments, optimal policies may be statistically indistinguishable from suboptimal ones even with infinite data and perfect function approximation. Through a set of minimal counterexample Markov decision processes (MDPs), we identify three distinct structural failure modes: (i) prefix indistinguishability leading to identifiability failure, (ii) objective misspecification induced by truncated returns, and (iii) offline dataset support and representation aliasing. Our results establish necessary conditions under which horizon reduction can be safe and highlight intrinsic limitations that cannot be overcome by algorithmic improvements alone, complementing algorithmic work on conservative objectives and distribution shift that addresses a different axis of offline RL difficulty (Fujimoto et al., 2019; Kumar et al., 2020; Gulcehre et al., 2020).
Paper Structure (41 sections, 3 theorems, 14 equations, 3 figures)

This paper contains 41 sections, 3 theorems, 14 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Contributions.
  3. Preliminaries
  4. Markov Decision Processes
  5. Offline Reinforcement Learning
  6. Horizon Reduction
  7. Horizon Reduction as Information Loss
  8. Counterexamples
  9. Prefix-Indistinguishable Commitment
  10. MDP construction.
  11. Offline dataset.
  12. Proof sketch.
  13. Short-Segment Optimality Violation
  14. MDP construction.
  15. Rewards.
  16. ...and 26 more sections

Key Result

Proposition 1

For the MDP described above and any learning algorithm whose decision rule depends only on the distribution of length-$H$ trajectory segments in the dataset, the actions $L$ and $R$ at $s_0$ are statistically indistinguishable. Consequently, no such algorithm can be guaranteed to select the optimal

Figures (3)

  • Figure 1: Prefix-indistinguishable commitment. Both initial actions $(L)$ and $(R)$ lead to identical length-$H$ trajectory windows along the shared chain. The value difference induced by the initial action is only revealed at step $H+1$, outside the reduced horizon.
  • Figure 2: Short-segment optimality violation. Greedy actions yield higher immediate rewards on every length-$H$ segment but incur a delayed penalty beyond the reduced horizon. Optimizing the truncated objective selects a policy that is globally dominated under the true return.
  • Figure 3: Offline support and representation aliasing. Although distinct long-term trajectories exist in the MDP, representation aliasing and windowed offline training collapse the two branches within the reduced horizon. Length-$H$ trajectory segments exclude the disambiguating states, rendering the optimal action unidentifiable.

Theorems & Definitions (4)

  • Proposition 1: Prefix indistinguishability
  • Proposition 2: Short-segment optimality violation
  • Proposition 3: Offline support-induced indistinguishability
  • Definition 1: $H$-sufficiency