Self-Supervised Goal-Reaching

• Self-supervised goal-reaching is a paradigm where agents learn to achieve desired outcomes by maximizing mutual information between current and goal states using intrinsic signals.
• Curriculum and goal diversity techniques, such as state-covering and conditional sampling, enable efficient exploration in high-dimensional, sparse-reward environments.
• Contrastive learning, auxiliary tasks, and learned functional distances collectively improve sample efficiency and long-horizon planning in robotics and multi-agent systems.

Self-supervised goal-reaching is an approach to sequential decision-making and control in which autonomous agents learn to reach user-specified outcomes by leveraging intrinsic signals and auxiliary objectives, rather than hand-engineered external rewards or extensive supervision. This paradigm has become central to modern robotics and reinforcement learning research, particularly in settings involving sparse rewards, high-dimensional observations, and challenging exploration requirements. Core techniques include contrastive reinforcement learning, curriculum and goal distribution design, self-supervised auxiliary tasks, learned functional distances, and architectural innovations for partial observability and long-horizon planning.

1. Core Principles of Self-Supervised Goal-Reaching

Self-supervised goal-reaching recasts the objective of policy learning from reward maximization to maximizing the likelihood or coverage of commanded goals in the state (or observation) space. The agent's task is defined through goal specification—often an image, state vector, or semantic descriptor—rather than a scalar reward function. The learning signal arises via intrinsic auxiliary objectives, information-theoretic measures, or structural properties of the environment, such as mutual information between current and goal states, entropy of sampled goals, or success indicators when a state matches a goal.

A representative mathematical formalism is provided by (Pong et al., 2019): the agent seeks to maximize the mutual information $I(s;G) = H(G) - H(G|s)$, where $s$ is the agent's achieved state and $G$ is the goal. This requires both learning reliable reaching policies (minimizing $H(G|s)$) and maximizing goal diversity (maximizing $H(G)$), often implemented through contrastive learning or entropy-maximizing goal samplers.

Crucially, self-supervised goal-reaching does not depend on external, task-specific reward engineering. Instead, it employs self-generated targets, auxiliary prediction tasks, or representations constructed from the agent's own exploratory rollouts as the supervisory signal.

2. Goal Setting, Curriculum, and Diversity

A central challenge is generating appropriate goals for self-practice—goals must be both feasible and diverse to support curriculum learning and avoid collapse to trivial or unachievable states. Multiple strategies have been established:

• State-Covering and Entropy-Maximizing Goal Samplers (Pong et al., 2019): Skew-Fit progressively updates a generative model of goal states by giving higher weight to rarely visited states. The weighting function $w_t(s) \triangleq q^{g}_t(s)^\alpha$ (with $\alpha < 0$) increases the probability of sampling under-explored states. This process provably converges to uniform exploration of the valid state space, maximizing coverage and efficiency.
• Conditional and Contextual Goal Sampling (Nair et al., 2019): In visually diverse or compositional tasks, context-dependent goal sampling constrains the proposed goals to those that are compatible with the current environment or scene. Conditional variational autoencoders use the initial observation as a context during goal encoding, ensuring that practiced goals are likely achievable and relevant given the available objects.
• Automatic Curricula via Dynamical Distance Functions (Prakash et al., 2021, Raparthy et al., 2020): Curriculum approaches generate a sequence of goals based on the estimated dynamical distance—e.g., the expected timesteps to reach the goal. The DDF is learned in a self-supervised fashion and is used to select goals that are challenging yet reachable, enabling the curriculum to adapt as the agent improves.
• Self-Play and Domain Randomization (Raparthy et al., 2020): Methods such as SS-ADR couple goal and environment curricula: one policy sets goals, another executes them under actively randomized environment parameters, and both curricula progress as agents master easier goals and environments.

These curriculum and diversity mechanisms have been empirically shown to dramatically accelerate sample efficiency and final task success, especially in high-dimensional domains with sparse external feedback.

3. Auxiliary Objectives and Functional Distances

When external rewards are sparse or unavailable, self-supervised auxiliary tasks supply dense, informative gradients:

• Prediction-based Auxiliary Losses (Khan et al., 2018): Auxiliary tasks such as next-state prediction ($L_{SP}$), reward prediction ($L_{RP}$), and executed-action prediction ($L_{AP}$) are trained alongside the main policy. These losses can be used both as direct regularizers for the learned representations and as sources of pseudo-rewards that augment the sparse environment reward, improving exploration and sample efficiency.
• Contrastive Learning and Representation Shaping (Zheng et al., 2023, Wang et al., 19 Mar 2025): Contrastive RL uses InfoNCE or noise-contrastive estimation objectives to drive the representations of current state–action pairs and desired goals together if related, pushing others apart. The critic functions are often structured as $f_{\phi,\psi}(s,a,g) = \|\phi(s,a)-\psi(g)\|_2$. This mechanism provides a self-supervised, temporally sharp learning signal, which is particularly effective for sparse reward environments and supports goal-conditional generalization.
• Self-supervised Reward Shaping via Embeddings (Mezghani et al., 2023): Dense reward functions are constructed by computing distances in learned, self-supervised latent spaces: $r(s,g) = -\|f(s) - f(g)\|_2$, where $f(\cdot)$ is an embedding network capturing task-relevant environment structure.
• Dynamical/Functional Distance Learning (Tian et al., 2020): Functional similarity is measured as the minimal expected number of timesteps needed to reach the goal from a given state, operationalized as a Q-function $Q(s, a, g) = \gamma^{d(s,a,g)}$. This supports planning over long or noisy horizons and aligns the value function learning with true dynamical reachability, outperforming naïve pixel-space metrics especially in manipulation and navigation tasks.

4. Architectures, Partial Observability, and Long-Horizon Planning

Self-supervised goal-reaching is distinguished by architectures adapted for partial observability, memory, and compositionality:

• Convolutional Encoders and Value Iteration Networks (Khan et al., 2018): For mobile robots with sparse range finder data, convolutional encoders extract geometric features. Value Iteration (VI) modules approximate classical value iteration in a convolutional architecture to generate local policies.
• Differentiable Memory (DNM, DNC) (Khan et al., 2018): In partially observable domains (e.g., long corridors or occluded rooms), integrating learned differentiable memory—via LSTM controllers with external read/write—enables agents to aggregate historical context for globally consistent planning.
• Deep Residual Networks and Scaling (Wang et al., 19 Mar 2025): Recent evidence highlights the importance of network depth: scaling critic networks from 4 to 1024 layers leads to 2x–50x improvements in success rates and unlocks qualitatively novel behaviors, such as humanoid agents learning to walk upright or perform acrobatic goal-directed movements. Deeper networks exploit richer, non-local representational structure, and improved performance arises via more global, less myopic planning.
• Hierarchical Policy Decomposition (Park et al., 2023): Decomposing goal-reaching into high-level latent subgoal selection (action-free) and low-level control to reach those subgoals mitigates the value learning noise associated with distant goals and allows incorporation of large quantities of action-free data for improved scalability and robustness.

5. Applications in Robotics, Multi-Agent Systems, and Real-World Deployment

Self-supervised goal-reaching underpins a broad cross-section of applications:

• Mobile Robot Navigation (Khan et al., 2018, Kahn et al., 2020): Robots trained via self-supervised auxiliary objectives and differentiable memory systems can efficiently reach specified targets under extreme sensory sparsity and partial observability, converging orders of magnitude faster than baseline policy gradient methods.
• Robotic Manipulation and Visual Planning (Tian et al., 2020, Mezghani et al., 2023, Zheng et al., 2023): Agents using functional distances, dense reward shaping, and contrastive RL successfully solve diverse manipulation tasks (pushing, reaching, object rearrangement) directly from images or raw states and with no hand-specified reward, demonstrating improved sample efficiency and compositional skill transfer.
• Precision Table Tennis and Continuous Imitation Learning (Ding et al., 2022): Iterative self-supervised goal-reaching based on relabeling and self-practice enables competitive performance (on par with or exceeding amateur humans) on dynamic tasks such as table tennis, with high sample efficiency and robustness on real robots.
• ObjectNav and In-Situ Finetuning (Min et al., 2022): Self-supervised contrastive learning leveraging location consistency enables robust semantic mapping and navigation in simulated and real household environments, outperforming supervised mesh-annotated methods in real-world transfer.
• Multi-Agent Coordination and Exploration (Nimonkar et al., 12 Sep 2025, Wang et al., 5 Mar 2024): Multi-agent systems adopting a self-supervised goal-reaching formulation—maximizing the probability of synchronously reaching joint goal states—demonstrate strongly emergent cooperative and exploratory behavior. Consensus mechanisms via imagined goals, modeled by generative CVAEs or contrastive representations, enable agents to coordinate efficiently even in environments where traditional MARL methods fail to achieve any reward.

6. Empirical Findings and Performance Impact

Self-supervised goal-reaching architectures and algorithms consistently demonstrate strong empirical advantages:

• Simulation and Real-World Results (Khan et al., 2018, Pong et al., 2019, Kahn et al., 2020, Ding et al., 2022, Zheng et al., 2023, Wang et al., 19 Mar 2025):
  • Sample efficiency improvements, in some cases converging in an order of magnitude fewer interactions.
  • Notable increases in success rate (up to 95% in real-world visual tasks (Pong et al., 2019); 2x–50x improvement over shallow models (Wang et al., 19 Mar 2025)).
  • Effective transfer from simulation to real robots (BADGR, ObjectNav, GoalsEye).
  • Emergent cooperation and exploration in multi-agent settings without explicit exploration incentives.
• Challenges and Open Issues:
  • Goal specification and representation selection remain important and sometimes delicate design choices (Nimonkar et al., 12 Sep 2025).
  • Theoretical understanding of why contrastive/self-supervised representations induce directed exploration and emergent cooperation in MARL is an ongoing research area.
  • While decoupling into independent agents accelerates early learning, there may be long-term tradeoffs in representational bias versus variance (Nimonkar et al., 12 Sep 2025).

7. Implications, Limitations, and Future Directions

Self-supervised goal-reaching fundamentally reduces the human engineering burden in robotics and reinforcement learning, shifting the focus from task-specific reward shaping to robust, generalizable representation, exploration, and planning frameworks. The demonstrated scalability with network depth and the emergence of complex, high-level behaviors as models grow point toward self-supervised RL as a potential foundation for highly capable, generalist autonomous agents—analogous to the impact of scale in language and vision domains (Wang et al., 19 Mar 2025).

Key areas for ongoing research include further depth and batch size scaling, distributed and resource-efficient training architectures, theoretical analysis of emergent exploration and credit assignment, hybridization with auxiliary tasks, and extension to lifelong, in-situ, and multi-agent continual learning contexts.

In summary, self-supervised goal-reaching provides a rigorous, empirically validated pathway toward general-purpose skill acquisition, scalable exploration, and flexible autonomy in high-dimensional, partially observed, and multi-agent environments, with enduring implications for both foundational research and deployed intelligent systems.