Goal-Dependent Learning

• Goal-dependent learning is a framework where agent policies and value functions are explicitly conditioned on goals, enabling efficient adaptation across diverse tasks.
• It utilizes techniques like curriculum design, experience relabeling, and goal representation to improve exploration and transfer learning in complex environments.
• This paradigm integrates insights from AI, cognitive science, and neuroscience to advance adaptive learning through dynamic value assignment, representation compression, and autonomous goal discovery.

Goal-dependent learning is a class of learning processes, algorithms, and cognitive phenomena wherein an agent’s value assignment, representation construction, exploration, and behavioral policy are dynamically shaped by explicit or implicit goals. In artificial intelligence, goal-dependent learning commonly refers to computational and algorithmic solutions where the learning signal, policy conditioning, or state representations adapt in accordance with user-specified or autonomously generated goals, ranging from simple position targets in robotic spaces to abstract conceptual outcomes in cognitive science. This paradigm extends traditional reinforcement learning—which typically optimizes for a fixed scalar reward—by requiring the agent to generalize, transfer, and efficiently solve a potentially large variety of goal-specified tasks.

1. Goal Representation and Conditioning

A core principle of goal-dependent learning is the explicit representation and conditioning of policies or value functions on goals:

• In continuous control tasks, goals are typically encoded as real-valued vectors $g \in \mathbb{R}^n$, where each dimension represents a subgoal or spatial coordinate (Eppe et al., 2018). For discrete and high-dimensional problems, goals may take the form of symbolic predicates, images, or language instructions (Liu et al., 2022).
• Goal-augmented Markov Decision Processes (GA-MDPs) define the formal foundation, specifying dynamics over $(s_t, a_t, g)$ with rewards $r_g(s_t, a_t, g)$ that depend explicitly on goal achievement (Liu et al., 2022).
• Modern architectures often prepend or embed the goal into the policy and value function input, enabling learning and generalization across multimodal and task-variant goals (Reuss et al., 2023, Levine et al., 2022). Methods such as Universal Value Function Approximators (UVFA) extend value functions to $V^\pi(s, g)$.

Goal representation is thus central to both learning signal assignment (e.g., sparse indicators or shaped distances) and the structural generalization required in multi-task and continual learning systems.

2. Curriculum, Sampling, and Difficulty Estimation

Learning efficiency in goal-dependent settings is strongly affected by how goals are sampled and sequenced during training:

• Curriculum Goal Masking (CGM) achieves adaptive curriculum design by masking subgoals and systematically modulating task difficulty, dynamically transitioning agents from easy to hard variants (Eppe et al., 2018). The masking vector $m \in \{0,1\}^n$ is applied to $g$, yielding $g_t^m = g \odot m + o_t \odot (1 - m)$, where $o_t$ denotes the current observation.
• Difficulty is estimated via recent success rates per mask, often under independence assumptions. Sampling masks according to proximity to a target success rate $c_g$ (the “Goldilocks zone”) is formalized as $p_g \propto |c_m - c_g|^\kappa$, focusing training on challenges that maximize learning progress (Eppe et al., 2018).
• Dynamical distance functions predict the expected (discounted) number of steps to achieve a goal from a candidate state, $d^\pi(s, s')$, and are used to automatically generate a curriculum of goals at the edge of the agent's current abilities (Prakash et al., 2021).
• Ensemble-based uncertainty estimation enables adaptive multi-goal exploration, such as AdaGoal, which maximizes value prediction error (ensemble disagreement) within a reachable radius to drive exploration toward uncertain, yet feasible, goals (Tarbouriech et al., 2021).

These mechanisms balance exploration and exploitation and can greatly improve sample efficiency in sparse reward and large goal space domains.

3. Goal-Dependent Value Learning and Successor Representations

A central technical challenge in goal-conditioned RL is learning goal-dependent value functions and representing the long-term outcome relevance of arbitrary goals:

• Temporal-difference (TD) updates are extended to goal-parameterized values $Q(s, a; g)$ and successor state operators $M$, which encode the (discounted) expected future state occupancy for a given goal or policy (Blier et al., 2021).
• Mathematical analysis reveals that successor states admit both forward and backward BeLLMan equations, and allow contraction mappings for convergence guarantees. BeLLMan-Newton (BN) operators, being second order, accelerate convergence but increase variance.
• Factorized representations, e.g., $M(s_1, s_2) \approx F(s_1)B(s_2)$, allow scalable, low-variance estimation in high-dimensional or continuous spaces.
• Goal-conditioned Q-learning is interpretable as a knowledge distillation problem, where both Q-functions and their gradients with respect to goals are matched via gradient-based attention transfer, improving performance, particularly in high-dimensional goal spaces (Levine et al., 2022).

These approaches enable efficient value-based planning in large, structured, or continuous goal spaces, and underpin advanced goal-conditioned deep RL algorithms.

4. Self-Imitation, Hindsight, and Relabeling Mechanisms

Learning from the agent’s own trajectories—irrespective of externally provided rewards—is a recurring theme:

• Hindsight Experience Replay (HER) extends the training set by relabeling failed trajectories with alternative achieved goals, transforming “failures” into “successes” for other goals (Liu et al., 2022). This maximizes data reuse, crucial for environments with rare rewards.
• Goal-Conditioned Supervised Learning (GCSL) and its extensions (WGCSL, GCSL-NF) cast the policy learning problem as maximizing the likelihood of actions leading to achieved (hindsight) goals, iteratively relabeling self-generated experience (Yang et al., 2022, Zhang et al., 3 Sep 2025). Weighted forms—such as WGCSL—introduce discounting, goal-conditioned advantage weighting, and best-advantage gating to ensure monotonic policy improvement, applicable both online and offline.
• Recent variants integrate negative feedback via contrastive learning, so that the agent also learns from failures, using a learned distance function $p_\phi(s_T, g)$ to guide exploration away from suboptimal behaviors (Zhang et al., 3 Sep 2025).

Collectively, these relabeling and self-imitation strategies substantially improve policy coverage and robustness by leveraging both positive and negative experience in a goal-sensitive context.

5. Goal-Driven Representation Learning, Compression, and Transfer

Beyond learning a policy for explicitly stated goals, agents can adapt their internal representations, value assignment, and even task abstraction in a goal-dependent manner:

• Theoretical frameworks posit that state representations, or “telic states,” emerge as equivalence classes of experience distributions that are equally desirable under a goal (Amir et al., 2023, Amir et al., 20 Aug 2025). Mathematically, $\mathcal{S}_g = \Delta(\mathcal{H})/\sim_g$, where $\sim_g$ partitions histories by their goal value equivalence.
• Goal-dependent compression of reward functions is a proposed human mechanism: working memory initially supports storing and comparing complex goal-outcome mappings, but with repeated exposure, this mapping is compressed into a concise rule and stored in long-term memory, allowing for automatic value assignment and improved efficiency (Molinaro et al., 8 Sep 2025).
• Empirical findings indicate that learning efficiency for abstract goals is parametrically impaired by the goal space size and improves with compressibility. Optimal goal-dependent performance correlates with faster reward evaluation, suggesting efficient representation transfer.
• These ideas also inform the paper of intrinsic motivation and the design of behavioral interventions: structuring goals to facilitate rule compression enhances both motivation and learning outcomes.

This body of work bridges cognitive science, neuroscience, and reinforcement learning in identifying and formalizing how representations and value systems co-evolve with an agent’s goals.

6. Applications, Transfer, and Adaptive Goal Discovery

Goal-dependent learning frameworks have been widely applied and extended:

• Robotic object manipulation tasks illustrate the efficacy of curriculum design, self-adaptive imitation (Goal-SAGAIL), and meta-imitation learning, especially when demonstration data are limited or suboptimal (Kuang et al., 15 Jun 2025, Eppe et al., 2018).
• Multimodal goal-conditioned policies—such as score-based diffusion architectures (BESO)—enable expressive generation of diverse behaviors, robust to the multi-modality present in play data and uncurated demonstrations (Reuss et al., 2023).
• Autonomous goal discovery and adaptation: Curiosity-driven architectures employing mechanisms such as dynamic neural fields and motor babbling, with inhibition of return, facilitate flexible exploration and self-generation of new skills in unconstrained environments (Houbre et al., 29 Nov 2024).
• Lifelong and open-ended learning: Goal discovery processes driven by intrinsic signals and open-ended generators expand the agent's skillset over an unbounded goal space, supporting continual and developmental learning trajectories (Sigaud et al., 2023).

In AI-driven education, multi-agent LLM-powered Intelligent Tutoring Systems have adopted goal-dependent learning for personalized, skill-targeted instruction, using dynamic skill gap identification, learning path optimization, and content personalization (Wang et al., 27 Jan 2025).

7. Theoretical and Practical Frontiers

Recent work unifies descriptive and prescriptive components in a world model by positing that state representations and reward assignment co-emerge from the agent's goals, inspired by both Bayesian formalism and epistemological traditions (Amir et al., 20 Aug 2025, Amir et al., 2023). This leads to general formulations where the policy is updated to minimize the Kullback–Leibler divergence between observed behavioral experience and distributions corresponding to desirable (goal-equivalent) states: $$\theta_{t+1} = \theta_t - \eta \nabla_\theta D_{KL}(P^* \| P_{\pi_\theta})$$ where $P^*$ is the projection onto the goal-equivalent class.

Open questions persist regarding the automatic discovery of new, structured goals, efficient goal-sampling strategies in non-stationary spaces, the interplay of self-imitation and negative feedback, and the principled selection or emergence of compressed reward functions supporting human-like intrinsic motivation and sustained performance.

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Overall, goal-dependent learning encompasses algorithmic, representational, and cognitive principles that allow agents to efficiently acquire, generalize, and transfer behaviors in the pursuit of diverse and potentially novel goals, through adaptive value assignment, curriculum design, experience relabeling, goal discovery, and representation compression.