Goal-Equivalent Experience Distributions

• Goal-equivalent experience distributions are defined as sets of agent-environment interaction sequences that, despite differing details, equally advance a specified goal.
• Telic states formalize these distributions by grouping experiences into equivalence classes based on goal relevance, enabling dynamic state abstraction.
• The framework integrates statistical divergence measures with reinforcement learning to align policies with goal-sensitive experience clusters, promoting robust adaptation.

Goal-equivalent experience distributions are formalized as the sets or classes of agent-environment interaction sequences (experiences) that—while possibly differing in many details—are equally effective (with respect to a specified goal) in enabling purposeful behavior. This concept operationalizes the equivalence of experiential histories from the agent’s point of view, providing a unified basis for learning, generalization, and the emergence of state representations and control. Recent computational frameworks have rooted this construct in both statistical and reinforcement learning settings, notably introducing the notion of telic states as equivalence classes over experience distributions that share goal-relevant properties.

1. Foundations: Goal-directed State Representation and Co-emergence

Canonical computational accounts, such as reinforcement learning, traditionally separate the world model into state representations (descriptive aspects) and reward functions (prescriptive aspects). The goal-equivalent experience distribution paradigm, however, formalizes an alternative in which state representations and evaluative functions co-emerge interdependently from the agent’s goals via interaction sequences. This approach situates the descriptive (what is) and the prescriptive (what is desirable) as jointly arising from preferences over experience distributions, rather than as pre-coupled or separate information flows.

As an agent accrues sensorimotor experiences (histories of actions and observations), it does not merely build an unbiased description of the world and later superimpose goals; instead, goals immediately inform which dimensions of experience are behaviorally relevant. The agent thus develops a representational apparatus that adapts dynamically to its motivational structure, partitioning experiences by their efficacy in advancing toward its current objectives. This process underpins the equivalence of experience distributions defined not on the totality of their sensory content, but on their functional relationship to the agent’s goal.

2. Telic States: Formalizing Goal-equivalent Experience Distributions

The key construct emerging from this paradigm is the telic state, defined as the equivalence class over distributions of experiential histories with respect to a given goal. For a goal specified as a binary preference relation $\succeq_g$ over the simplex of possible experience distributions $\Delta(\mathcal{H})$, the telic state space is

$\mathcal{S}_g = \Delta(\mathcal{H}) / \sim_g$

where $A \sim_g B$ if $A$ and $B$ are equally preferred by the agent for the goal $g$.

For each goal $g$, telic states $\mathcal{S}_g$ group together those experience distributions that do not differ in respects that matter to the accomplishment of $g$. Telic states are thus sufficient statistics for goal-directed control and generalization. The state abstraction is adaptive: by modulating which features of experience are grouped together as "equivalent," the agent can flexibly ignore goal-irrelevant details, supporting transfer, compression, and goal-based partitioning of the environment.

3. Statistical Divergence and Policy Alignment

The alignment of an agent’s policy with desirable telic states is quantified using divergence measures, particularly the Kullback–Leibler divergence. If $\pi$ denotes the agent’s policy and $P_\pi$ the induced distribution over experience trajectories, the telic distance to a desired telic state $S_i$ is defined by

$R = \min_{P\in S_i} D_{KL}(P \parallel P_\pi)$

where $D_{KL}$ is the KL divergence. This distance captures, in the information-theoretic sense, how “goal-equivalent” the agent’s actual experiences are relative to the most preferred (optimal) distributions.

Learning algorithms can be formulated to minimize this distance. For example, policy updates via the policy gradient

$$\theta_{t+1} = \theta_t - \eta \nabla_\theta D_{KL}(P^*_i \parallel P_{\pi_\theta})$$

with $$P_i^* = \arg\min_{P\in S_i} D_{KL}(P \parallel P_{\pi_\theta})$$, adjust parameters $\theta$ so that the distribution of generated experiences approaches the telic state.

This approach generalizes the reward-maximization objective to an information-geometric regime: policies are adapted not only for local reward, but to minimize a holistic discrepancy between observable experience and goal-equivalent distributions.

4. Empirical and Theoretical Literature

The telic state and goal-equivalent distribution framework is rooted in both empirical and theoretical strands:

• Empirical support arises from studies showing that agents (biological and artificial) remap and restructure their state spaces in response to goal changes, as observed in hippocampal or orbitofrontal recoding.
• Theoretical tools are drawn from Bayesian inference, predictive coding, and active inference, where the primary objective is to organize perception and action around the minimization of global prediction error or uncertainty with respect to internally generated expectations (desirable outcomes).

The framework is illustrated with concrete models:

• In the two-armed bandit, policies guided by minimizing telic distance recover probability matching as the optimal behavior.
• In navigation tasks, telic states correspond to sets of routes grouped by their efficiency in reaching the goal, abstracting away the microstructure of individual paths.

Additionally, formal pseudocode and explicit mathematical definitions are provided in the source, including the update mechanics for learning to minimize KL divergence to the telic state.

5. Applications and Unified Perspectives

The implications of goal-equivalent experience distributions are wide-ranging:

• In neuroscience, telic states offer a model for how animals and humans may flexibly adapt their cognitive maps and behaviors to new goals, rather than using globally fixed state partitions.
• For artificial agents, telic state representations enable hierarchical abstraction, transferability, compression, and multi-objective learning by modulating the granularity of experience clustering as the goals change.
• In robotics and control, this approach facilitates robust generalization: robots equipped with telic state abstractions focus on task-relevant dimensions of experience, enhancing adaptation to new tasks or environmental changes.

By coupling descriptive and prescriptive aspects, the framework provides a unified account that links behavioral strategies, representational learning, and underlying neural or computational processes.

6. Mathematical Formulations and Algorithms

Key mathematical constructs for this paradigm are:

• Telic state equivalence:

$\mathcal{S}_g = \Delta(\mathcal{H}) / \sim_g$

where $\sim_g$ arises from goal-induced equivalence.

• Telic distance (KL divergence to goal-equivalent class):

$R = \min_{P\in S_i} D_{KL}(P \parallel P_\pi)$

• Policy update to minimize telic distance:

$$\theta_{t+1} = \theta_t - \eta \nabla_\theta D_{KL}(P^*_i \parallel P_{\pi_\theta})$$

• Probability-matching in the two-armed bandit (as given by expectation over telic-optimal histories):

$$\theta^*_j = \mathbb{E}_{h \sim P^*_j}\left(\frac{N^h_L}{N^h_L+N^h_R}\right)$$

These formulas show how experience distributions are mapped, clustered, and optimized with respect to agent goals.

7. Synthesis and Broader Significance

The framework of goal-equivalent experience distributions, operationalized through telic state representations and statistical divergence objectives, establishes a new paradigm in which the structuring of experience, representation, and control are entwined with agent goals from the outset. This paradigm supports parsimonious, adaptive accounts of learning that unify behavioral, phenomenological, and neural dimensions of purposeful behavior. It opens avenues for goal-driven state abstraction, dynamic generalization, and more flexible forms of artificial intelligence and autonomous agency—markedly advancing the theoretical understanding of purposeful behavior and the practical realization of goal-sensitive learning systems (Amir et al., 20 Aug 2025).