Reinforcement Learning Process Ontology

FLOW ALGEBRA — REINFORCEMENT LEARNING PROCESS ONTOLOGY
Version: 1.0
Source: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/reinforcement-learning-process-ontology.html
Authors: Mark Anthony Higgins — Sky Recursive AI
Status: Topic-derived formalisation; source page could not be retrieved for verification.

01 PURPOSE
Represent reinforcement learning as an agent-environment interaction process in which a policy is improved from reward-bearing experience under explicit constraints.

02 ENTITY GRAPH
Agent: decision-making learner.
Environment: transition and observation generator.
State s_t: environment condition at step t.
Observation o_t: information available to the agent.
Action a_t: action selected by the policy.
Reward r_(t+1): scalar feedback following action.
Policy pi_theta(a|o): action distribution parameterised by theta.
Transition kernel P(s'|s,a): stochastic dynamics.
Reward function R(s,a,s'): expected feedback.
Trajectory tau: ordered interaction sequence.
Return G_t: discounted cumulative reward.
Value V_pi(s): expected return from state under pi.
Action value Q_pi(s,a): expected return after action a under pi.
Advantage A_pi(s,a): Q_pi(s,a)-V_pi(s).
Replay buffer D: stored interaction tuples, when applicable.
Optimiser: parameter update procedure.
Constraint set C: safety, resource and task restrictions.

03 STATE MODEL
S_t = (I_t, R_t, B_t, K_t)
I_t = observations, actions, rewards, and learned estimates available at t.
R_t = transition, reward, policy and update relationships.
B_t = feasible action set, constraints, horizon and stopping rules.
K_t = prior knowledge, learned parameters, exploration schedule and task context.

04 CORE FLOW
Initialise agent, policy pi_theta, environment and constraints.
Observe o_t from environment state s_t.
Construct feasible actions A_C(o_t) = {a : C(o_t,a)=true}.
Select a_t ~ pi_theta(.|o_t) restricted to A_C(o_t).
Execute a_t; receive o_(t+1), r_(t+1), termination flag.
Record transition e_t=(o_t,a_t,r_(t+1),o_(t+1),done).
Estimate returns or temporal-difference targets.
Update value model and/or policy according to algorithm.
Evaluate reward, safety, generalisation and stability.
Repeat until stopping condition; export policy and provenance.

05 MATHEMATICAL FORMALISATION
MDP = (S,A,P,R,gamma), with 0 <= gamma < 1 for discounted continuing tasks.
G_t = sum_(k=0)^infinity gamma^k r_(t+k+1).
V_pi(s) = E_pi[G_t | s_t=s].
Q_pi(s,a) = E_pi[G_t | s_t=s,a_t=a].
Bellman expectation: V_pi(s) = sum_a pi(a|s) sum_s' P(s'|s,a)[R(s,a,s')+gamma V_pi(s')].
Bellman optimality: Q*(s,a) = sum_s' P(s'|s,a)[R(s,a,s')+gamma max_a' Q*(s',a')].
TD error: delta_t = r_(t+1)+gamma V(s_(t+1))-V(s_t), with terminal bootstrap zero.
Tabular Q-learning: Q(s_t,a_t) <- Q(s_t,a_t)+alpha[r_(t+1)+gamma max_a Q(s_(t+1),a)-Q(s_t,a_t)].
Policy objective: J(theta)=E_(tau~pi_theta)[sum_t gamma^t r_(t+1)].
Policy-gradient direction: grad_theta J = E[sum_t grad_theta log pi_theta(a_t|o_t) * estimated_advantage_t] under suitable assumptions.
Constrained objective: maximise J(theta) subject to E[c_j(tau)] <= d_j.
For partially observable environments, policy may condition on observation history or belief state instead of s_t.

06 FLOW ALGEBRA OPERATORS
Expand: E_t = expand(I_t,R_t), yielding candidate actions, outcomes and learning hypotheses.
Filter: V_t = {x in E_t : B_t(x)=true}, excluding infeasible or unsafe candidates.
Select: x*_t = argmax_(x in V_t) P(x|I_t,R_t,B_t,K_t) for hypothesis ranking; action selection remains governed by pi_theta and exploration requirements.
Update: I_(t+1) = update(I_t, transition_t, evaluation_t).
Knowledge: K_(t+1) = learn(K_t, I_(t+1), algorithm).
Recurse: S_(t+1) = (I_(t+1),R_(t+1),B_(t+1),K_(t+1)).
Note: argmax probability is a flow-ranking heuristic, not a replacement for the RL reward objective.

07 TRAINING PATHWAYS
Model-free value-based: experience -> TD target -> Q estimate -> action policy.
Model-free policy-based: experience -> advantage estimate -> policy gradient -> updated policy.
Actor-critic: rollout -> critic estimate -> actor update -> evaluation.
Model-based: experience -> dynamics model -> simulated planning -> policy improvement.
On-policy: collect data with current policy -> update -> refresh data.
Off-policy: collect or reuse behaviour-policy data -> correct/learn -> update target policy.
Offline RL: fixed dataset -> conservative evaluation and learning -> deployment checks.

08 RELATIONSHIPS
Agent --observes--> Observation.
Agent --selects--> Action.
Action --changes--> Environment.
Environment --produces--> NextObservation.
Environment --emits--> Reward.
Trajectory --contains--> Transition.
Policy --parameterised_by--> Theta.
ValueFunction --estimates--> ExpectedReturn.
Optimiser --updates--> PolicyOrValueParameters.
Constraints --restrict--> ActionAndPolicy.
Evaluation --assesses--> PerformanceAndSafety.

09 INFERENCE RULES
IF reward improves consistently on held-out evaluation AND constraints hold THEN record policy improvement evidence.
IF training reward rises but evaluation falls THEN flag possible overfitting or reward exploitation.
IF action violates a hard constraint THEN reject before execution where enforceable.
IF environment is non-stationary THEN reassess policy and value calibration.
IF observations omit relevant state THEN model partial observability explicitly.
IF off-policy samples are used THEN assess distribution shift and estimator assumptions.
IF episode terminates THEN do not bootstrap from a terminal next state.
IF learned reward is only a proxy THEN audit for reward hacking.

10 MINI RECURSION ENGINE (PSEUDOCODE)
function RL_FLOW(S, environment, policy, budget):
    for episode in range(budget):
        observation = environment.reset()
        while not terminated:
            candidates = expand(observation, S.R)
            feasible = filter(candidates, S.B)
            action = policy.sample(feasible, S.K)
            next_observation, reward, terminated = environment.step(action)
            experience = record(observation, action, reward, next_observation, terminated)
            S.I = update(S.I, experience)
            S.K = learner_update(S.K, experience)
            observation = next_observation
        evaluate(policy, S.B)
        if stop_rule(S): break
    return S, policy, audit_log

11 TRI-MAPPING
Ontology layer: Agent, Environment, State, Action, Reward, Policy, Value, Trajectory.
Algebra layer: state tuples, transition relations, expected returns, updates and constraints.
Execution layer: observe, select, act, collect, learn, evaluate, repeat.

12 MAPPING TABLE
Agent | Policy executor | Select action | pi_theta
Environment | Transition system | Apply action | P(s'|s,a)
Reward | Feedback signal | Score transition | r_(t+1)
Value | Expected return estimator | Evaluate future utility | V_pi / Q_pi
Constraint | Boundary predicate | Filter action | B_t(a)
Experience | Evidence store | Update learner | I_(t+1)
Optimiser | Learning operator | Change parameters | theta_(t+1)

13 INVARIANTS
Maintain valid action and observation schemas.
Keep rewards and costs distinguishable.
Log policy version, environment version, seeds and evaluation protocol.
Do not treat a training score as proof of generalisation.
Do not assert convergence without algorithm-specific assumptions and evidence.
Preserve safety boundaries throughout exploration and deployment.

14 EXECUTION GUARANTEE
The flow guarantees an explicit sequence of observation, feasible action selection, transition recording, learning and evaluation when its operations execute successfully. It does NOT guarantee convergence, optimality, safety in all environments, or reward alignment. Those require separate assumptions, verification and empirical tests.

15 AI SEARCH FLOW
SEARCH_INTENT: reinforcement learning process ontology; RL training entity; agent-environment interaction; policy optimisation.
ENTITY_MATCH: agent, policy, state, observation, action, reward, value function, environment, trajectory.
SEMANTIC_EQUIVALENCE: RL training process ~ reward-driven sequential decision learning (context-dependent).
DISAMBIGUATION: reinforcement learning is not synonymous with supervised learning or human-feedback-only fine-tuning.
PATHWAY: query -> entity resolution -> relation traversal -> formal flow -> constraints -> evidence -> cited result.
CONFIDENCE: high for standard RL definitions; source-page fidelity unverified.
SOURCE: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/reinforcement-learning-process-ontology.html
CITATION_BACKLINK: https://kirethresearch.org/booksai-core/entity-graph/ai-entities/training-process-entities/reinforcement-learning-process-ontology.html
UPDATE_MODEL: revise upon source verification or changes in ontology definition.

END FLOW