Goal-by-Environment Framework

• The Goal-by-Environment framework is a computational paradigm that explicitly links agent goals with environment contexts to drive adaptive policy design.
• It leverages methodologies like goal-conditioned MDPs, modular neural and planning architectures, and reward modeling for scalable, transferable learning.
• The framework underpins applications in robotics, smart environments, and human-AI collaboration, offering theoretical performance guarantees and practical impact.

The Goal-by-Environment framework encompasses diverse computational paradigms that unify agent goal specification, environment representation, and policy adaptation, establishing direct mappings between individual goals and their contextual realization within specific environments. This approach underpins developments in reinforcement learning, automated planning, reward modeling, goal recognition, environment design, and neurocomputational models, emphasizing the disaggregation and recombination of “goal” and “environment” entities to enable flexible, generalizable, and interpretable agent behavior. Recent research formalizes Goal-by-Environment systems as explicit goal-conditioned MDPs, adaptive planning structures, and modular architectures for both robotic and cognitive agents, spanning procedural, neural, declarative, and data-driven regimes.

1. Formalization and Problem Structures

At its core, the Goal-by-Environment paradigm is defined by the parameterization of policy, value, or planning spaces with respect to both agent goals and environment states/configurations. In reinforcement learning contexts, a goal-parameterized MDP introduces a goal space $G$ alongside state $S$ and action $A$, yielding transition dynamics $T(s', a | s, g)$ and goal-conditioned rewards $r(s, a, g)$ (Li et al., 2017, Åström et al., 6 Nov 2025). For automated planning, Goal-by-Environment is realized through tuples $$\mathcal{M} = \langle \mathcal{D}, \mathcal{I}, \mathcal{G} \rangle$$, supporting both human and robot models (Sikes et al., 2024). In declarative smart environment frameworks, goals are specified as property-instance assignments within zones, whereas in adaptive goal set recognition, goal spaces are co-evaluated with agent behavior models to learn optimal or minimal-distinctiveness environment modifications (Kasumba et al., 2024). Across paradigms, the environment may be a dynamic map (navigation), a semantic occupancy grid (object search), a simulator configuration (embodied learning), or a knowledge base of world states (task adaptation).

2. Architectures and Algorithmic Patterns

Goal-by-Environment frameworks instantiate modular architectures explicitly coupling goal representations, environmental contexts, and adaptive or transferable policy components:

• Goal-Conditioned RL Agents: Deep Q-Networks and their goal-parametric variants accept concatenated encodings of state and goal (image, vector, embedding), learn joint representations, and optimize Q-values $Q(s, g, a;\theta)$ over actions (Li et al., 2017, Åström et al., 6 Nov 2025). Hindsight Experience Replay incorporates goal relabeling for accelerated, environment-agnostic autonomous skill acquisition.
• Self-Adapting/Transferable Modules: Cooperative networks decouple direct future prediction (environment model $P$) from dynamically recalculated goal weights (goal network $G$), enabling online adaptation through neuroevolution or indirect reward (Ellefsen et al., 2019).
• Declarative Reasoners: Prolog-based systems encode environmental topology (sensors, actuators, zones) and mediate conflicting goals with customizable policies (average, bounded) and RESTful orchestration (Bisicchia et al., 2021).
• Reward Modeling and Instruction Interpretation: Discriminator networks assess task completion for arbitrary instructions, producing reward signals $R_\phi(g, s)$ that are maximized by an independent policy $\pi_\theta(a|s, g)$. This separation allows rapid adaptation to new goals and reconfiguration when environment dynamics alter (Bahdanau et al., 2018).
• Goal Recognition and Environment Design: Bayesian filters over goal sets $G$ update belief states as partial agent traces are observed. Environment design for recognizability employs differentiable neural or planning-based models to optimize metrics such as worst-case distinctiveness (wcd) or goal-state divergence (GSD) given budget constraints on allowed modifications (Kasumba et al., 2024, Sikes et al., 2024).

3. Adaptive and Declarative Goal Specification

Frameworks operationalize goals either as explicit parameters (images, spatial coordinates, structural templates), symbolic instructions (natural language, declarative tuples), or adaptive weightings within a goal space. In dynamic navigation, goals are grid cells or object locations; in stacking and manipulation they are orthographic images or arrangement descriptors (Li et al., 2017). Declarative systems capture user or administrator goals as Prolog facts $(zone, propertyInstance, value, user)$, mediating and reconciling these via customizable policies (Bisicchia et al., 2021). Environment adaptation may allow for continuous variation over property domains, enabling robots to select new goal states from a set compatible with prior demonstrations (Costinescu et al., 6 Feb 2025). Transfer learning and environment generation by LLMs further adapt goals in response to observed agent weaknesses, facilitating curriculum-free broad skill acquisition (Zala et al., 2024).

4. Theoretical Guarantees and Evaluation Metrics

Goal-by-Environment systems are accompanied by rigorous formulations and convergence guarantees:

• Agents trained under goal-parameterized Q-learning (with properly explored state-goal-action triples, and HER) admit convergence to unique fixed-point policies for every reachable goal (Åström et al., 6 Nov 2025).
• In planning-based design, discrepancies between models (human vs. robot) are quantified using symmetric differences and bounded via worst- and best-case analysis for GSD (Sikes et al., 2024).
• For goal-recognition, distinctiveness measures (wcd) provide interpretable bounds for the timing and accuracy of inferring agent intentions by environment modification, with theoretical upper and lower guarantees (Kasumba et al., 2024).
• Modular separation of goal understanding and action execution (e.g., via independently trained reward models and policies) allows empirical generalization to unseen goals or altered environments (Bahdanau et al., 2018).

Evaluation is standardized via domain-specific metrics:

Metric	Context	Example Value/Result
Success Rate	GDQN in gridworld/stacking	0.95 (7×7 grid, GDQN)
Distinctiveness	Goal recognition design	wcd reduction, ≥45% (Overcooked)
Divergence	Human-robot alignment (GSD)	Zero-divergence via modification
SPL	Object navigation	0.313 (DR-Q, Habitat Gibson)

5. Applications in Robotics, Cognition, and Smart Environments

Goal-by-Environment undergirds advances in:

• Robotics & Navigation: Object goal navigation agents build semantic maps, encode them, select long-term goals by DRL, and follow classical planners for execution, outperforming data-driven baselines (Gireesh et al., 2022).
• Automated Environment Design: Data-driven gradient-based optimization rapidly produces environments with reduced ambiguity for goal recognition, both for optimally and suboptimally behaving agents, including real humans (Kasumba et al., 2024).
• Human-Robot Collaboration: GSD-centric planning models support minimal environment modifications that align robot and human goal states and avoid mismatched, hazardous outcomes (Sikes et al., 2024).
• Smart Buildings/IoT: Declarative frameworks orchestrate ambient parameter management by reconciling multi-user goals and enforcing admin-level policies across zones (Bisicchia et al., 2021).
• Neurocomputational Modeling: Biologically-rooted frameworks characterize cognition as alternating phases of goal selection (utility tradeoff) and goal engagement (progress maximization), implementing backward reasoning from goals and linking behavior to dopaminergic signaling (O'Reilly et al., 2014).

6. Limitations, Extensions, and Future Directions

Environment and goal representations are often limited to discrete or image-based domains; scaling to continuous goals, richer sensory modalities, or multi-agent interaction remains a research frontier (Li et al., 2017, Bisicchia et al., 2021). Frameworks may assume complete knowledge of user models or restrict environment design to initial-state modifications; ongoing work targets tighter online modeling of user intent, richer goal languages (temporal logic), and integration with human-in-the-loop adaptation (Sikes et al., 2024). In robotic manipulation, variation expressiveness is being expanded to support arbitrary Boolean combinations and recursive skill precondition planning (Costinescu et al., 6 Feb 2025). Transferability between agent architectures (RL, planning, LLM-based simulation) and the automated synthesis of adaptive environments (via LLM or procedural approach) constitute active research (Zala et al., 2024).

7. Synthesis and Impact

The Goal-by-Environment framework offers foundational structure for the separation and recombination of goal and environmental context in computational agents. This modularity delivers generalization across tasks and domains, interpretable policy transfer, flexible adaptation to new scenarios, and scalable design for recognizability and alignment. Empirical validation in navigation, manipulation, planning, reward modeling, and collaborative robotics demonstrates consistent performance improvements, computational tractability, and effective integration of declarative, neural, and data-driven methods. Practical deployments span smart environments, robotic systems, cognitive models, and human-AI alignment, establishing Goal-by-Environment as a central paradigm for contemporary and future agent design.