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Foundations for Restraining Bolts: Reinforcement Learning with LTLf/LDLf restraining specifications
Giuseppe De Giacomo, Luca Iocchi, Marco Favorito, Fabio Patrizi
TL;DR
The paper asks how an RL agent can follow temporal restrictions expressed over features it does not observe. It combines RL with LTLf/LDLf restraining specifications and reports that, under general circumstances, the agent can learn policies that conform as much as possible while keeping the specification features separate.
Problem
The paper studies how an RL agent can conform to temporal restrictions expressed over a distinct feature set that the agent does not observe.
Source: Introduction · p. 1, RL with LTLf/LDLf restraining… · p. 4Method
The restraining bolt supplies LTLf/LDLf-based rewards and formula-stage features alongside the agent’s own RL representation.
Source: Introduction · p. 1, RL with LTLf/LDLf restraining… · p. 5Results
Under general circumstances, the agent can learn policies that conform as much as possible to the restraining specifications without including their features in its state space.
Source: Introduction · pp. 1–2Takeaways & Limitations
The features needed to evaluate the temporal formulas can remain separate from those directly accessible to the learning agent.
Source: Conclusions · p. 8Choosing the appropriate scaling factor for the restraining bolt’s rewards is outside the paper’s scope.
Source: Introduction · p. 1
Abstract
from arXiv · showhide
In this work we investigate on the concept of "restraining bolt", envisioned in Science Fiction. Specifically we introduce a novel problem in AI. We have two distinct sets of features extracted from the world, one by the agent and one by the authority imposing restraining specifications (the "restraining bolt"). The two sets are apparently unrelated since of interest to independent parties, however they both account for (aspects of) the same world. We consider the case in which the agent is a reinforcement learning agent on the first set of features, while the restraining bolt is specified logically using linear time logic on finite traces LTLf/LDLf over the second set of features. We show formally, and illustrate with examples, that, under general circumstances, the agent can learn while shaping its goals to suitably conform (as much as possible) to the restraining bolt specifications.
Introduction
The paper frames restraining-bolt reinforcement learning as a way to shape an agent’s behavior using temporal specifications over features the agent does not observe. It argues that the agent can learn to conform as much as possible without formalizing the relationship between the two feature sets.
Introduction
- The agent learns over its own world features, while the restraining bolt uses disjoint features to specify desirable traces and provide additional rewards.The bolt does not explicitly model world dynamics or the agent; it can assess generated traces and reward desirable ones.Source: Introduction · p. 1
- The connection is loose: the bolt’s additional rewards need only be scaled using the order of magnitude of the agent’s rewards, and formula-stage features let the agent adapt its policy.Choosing the scaling factor is outside the paper’s scope.Source: Introduction · p. 1
- Under general circumstances, an RL agent can learn to conform as much as possible to LTLf/LDLf specifications without representing their features in its state space.The agent’s and restraining bolt’s feature sets are distinct but correlated through the world; that correlation need not be formalized.Source: Introduction · pp. 1–2
Preliminaries
- LTLf is interpreted over finite traces, while LDLf extends it with regular-expression path expressions and tests for expressing procedural and declarative specifications.The formulas track satisfaction over traces and can be transformed into deterministic finite-state automata.Source: Preliminaries · p. 2
- LTLf/LDLf reward specifications can select traces and assign rewards through formula–reward pairs, avoiding an explicit non-Markovian reward function.The formulas’ propositions correspond to Boolean features or propositions over world features.Source: Preliminaries · p. 3
NMRDP with LTLf/LDLf rewards
The paper uses the established automata construction for LTLf/LDLf rewards to convert an NMRDP into an equivalent MDP. This construction preserves transitions and rewards, and policies in either representation have equivalent counterparts in the other.
NMRDP with LTLf/LDLf rewards
- The paper states that its results also apply to other finite-trace temporal formalisms, including Past LTL and co-safe LTL.The passage lists several additional formalisms.Source: NMRDP with LTLf/LDLf rewards · p. 3
- The equivalent MDP’s state space is the product of the original state space and the formula-automaton states, making its reward Markovian.The formula structure is compiled into the MDP states.Source: NMRDP with LTLf/LDLf rewards · p. 3
- An NMRDP with LTLf/LDLf rewards is equivalent to an MDP constructed by the stated automata-based transformation.The construction is based on the earlier result of Brafman, De Giacomo, and Patrizi (2018).Source: NMRDP with LTLf/LDLf rewards · p. 3
- Every policy for the constructed MDP has an equivalent non-Markovian policy for the NMRDP, and vice versa.The corresponding policy tracks the automata states while preserving rewards.Source: NMRDP with LTLf/LDLf rewards · p. 3
RL for NMRDP with LTLf/LDLf rewards
For NMRDPs with LTLf/LDLf trace rewards and hidden transitions, the paper reduces learning to an MDP whose transformed dynamics and rewards remain hidden. The learner can use standard MDP algorithms by treating that implicit transformed model as its working model.
RL for NMRDP with LTLf/LDLf rewards
- Because the transformed problem is an MDP, Q-learning or SARSA can obtain an optimal policy while the learner assumes the implicit transformed model.The original trace-based rewards do not fit typical MDP-based algorithms directly.Source: RL for NMRDP with LTLf/LDLf rewards · p. 3
- Theorem 3 reduces RL for NMRDPs with LTLf/LDLf rewards to RL over an MDP whose transitions and rewards remain hidden from the learner.The reduction is not performed explicitly during learning.Source: RL for NMRDP with LTLf/LDLf rewards · p. 4
- Although the transformed state records formula-satisfaction stages, hidden transitions prevent the agent from anticipating an action's effect before execution.The agent learns from sampled transitions rather than an explicitly constructed transformation.Source: RL for NMRDP with LTLf/LDLf rewards · pp. 3–4
RL with LTLf/LDLf restraining specifications
This section presents an MDP-based reinforcement-learning approach to hidden LTLf/LDLf restraining specifications, keeping specification-evaluation features separate from those accessible to the agent and using DFA-progress features and specification rewards. It describes a modular simulation-based implementation and reports experiments in which agents learn policies that follow the specifications, though satisfaction is not guaranteed.
RL with LTLf/LDLf restraining specifications
- Policies need only observe agent states and DFA progress, not the hidden fluent configurations used to evaluate the LTLf/LDLf formulas.The DFA states encode formula progress while the fluent configurations remain inaccessible to the learning agent.Source: RL with LTLf/LDLf restraining… · pp. 4–5
- Lemma 5 establishes that restricting learning to Markovian policies over agent and DFA states loses no generality.This replaces policies that depend on the full history of those states with policies depending only on the current combined state.Source: RL with LTLf/LDLf restraining… · p. 5
- Theorem 6 shows that the restraining-specification task can be learned through an MDP over agent states and DFA states, preserving optimal policies.The approach adds specification rewards at suitable times and DFA-state features, while leaving the underlying fluent configurations hidden.Source: RL with LTLf/LDLf restraining… · p. 6
Implementation and Examples
- The implementation separates a simulator, a restraining-bolt process, and an RL agent, which exchange states, DFA-progress encodings, actions, and rewards.Training occurs in simulation before policy execution in the real world; the setup assumes the simulator models relevant world dynamics.Source: Implementation and Examples · p. 6
- DFA-based reward shaping can anticipate rewards before a temporal formula is satisfied, while episode resets follow formula satisfaction, failure, or an action limit.Experiments end at problem-specific time limits chosen to ensure a specification-consistent policy is found, though not necessarily an optimal one.Source: Implementation and Examples · p. 6
- Breakout agents learned to progress through specification states, while Sapientino agents achieved score 14 for S2 and score 21 for S3.The same Breakout bolt shaped behavior for agents with different abilities; Sapientino used two agent types and two specifications.Source: Implementation and Examples · pp. 7–8, Figure 3 · p. 7
- In the cocktail-party simulator, the agent converged after about 1 minute to a policy satisfying the restraining specification, with score 4 for serving two people one drink and one snack each.The simulator modeled four tasks; optimized code could reduce the reported time.Source: Figure 3 · p. 7, Implementation and Examples · p. 8
- The approach also used the SAPIENTINO agent for 10 Minecraft tasks, with results reported as confirming that a general-purpose agent can learn tasks from its bolt.The cocktail-party bolt used identity, age, and received-item features distinct from the robot’s state representation.Source: Implementation and Examples · p. 8
Conclusions
- The method uses typical MDP-based reinforcement learning while keeping formula-evaluation features separate from those directly accessible to the learning agent.The bolt treats the agent as a black box and specifies constraints using its own world features, but does not guarantee their satisfaction during or after training.Source: Conclusions · p. 8
- Formal verification requires modeling how actions affect bolt features and linking the agent’s features to them, but reinforcement learning itself needs no such link because the world can provide it.Model checking is one option once that action-effect model is available.Source: Conclusions · p. 9
- Separate feature spaces support modularity and reuse: the same agent can learn from different bolts, while a smaller agent representation can still support complex declarative specifications.This separation also allows the agent’s features and goal features to be designed independently.Source: Conclusions · p. 9