Towards Constraint-Compliant, Multi-Objective Aligned LLM Feedback for STEM Education: Formal Methods, Algorithms, and Human-Grounded Benchmarks

NTU PhD Research Proposal
Edward Bird · e.bird@ucb.ac.uk
8 May 2026

Introduction

The quality of formative feedback is a well-established determinant of student learning outcomes, yet its delivery at scale remains a persistent practical problem in STEM education. Large language models (LLMs) offer the potential to provide personalised, immediate feedback across large student cohorts; however, current systems lack formal guarantees that their outputs conform to pedagogically appropriate behaviour. They may leak model answers, ignore marking rubrics, produce feedback at an inappropriate scaffold level, or systematically disadvantage certain student groups. Educators, institutions responsible for academic integrity, AI safety researchers, and the wider NLP community all have a direct stake in ensuring that automated feedback is verifiable, fair, and genuinely useful.

Despite rapid adoption of AI in education (Bond et al., 2024; Manorat et al., 2025; Apata et al., 2025), four critical gaps remain unaddressed. First, no existing approach enforces pedagogy-critical constraints during generation with formal correctness guarantees — post-hoc filters are incomplete and offer no assurance of constraint satisfaction. Second, alignment pipelines are typically trained against a single objective, leaving utility, compliance, and fairness in unresolved and unmeasured tension. Third, evaluation of AI-generated feedback relies predominantly on automated proxy metrics rather than human-grounded protocols that are reproducible and independently verifiable. Fourth, where human evaluation has been applied to open-ended assessment tasks, the most reliable method — comparative judgement — has not been applied to AI-generated feedback, leaving no established human-grounded benchmark for this domain.

This PhD directly addresses all four gaps. The central research question is: Whether and to what extent can large language models be designed and aligned to deliver safe, pedagogy-aligned formative feedback with verifiable constraint compliance, strong learning utility, and fair outcomes across student groups? The proposed work will investigate (1) a novel verifier-guided constrained decoding algorithm, examining its correctness properties and complexity characteristics; (2) a multi-objective alignment pipeline for jointly optimising competing educational objectives; and (3) a publicly released human-grounded benchmark for the field. These contributions are designed to generalise beyond education to any safety-critical text generation setting, making them of broad relevance to the AI and NLP research communities.

Literature Review

Constrained Generation

Early work on constrained decoding introduced grid beam search to enforce lexical constraints during sequence generation (Hokamp and Liu, 2017) and dynamic beam allocation to improve efficiency (Post and Vilar, 2018). More recent approaches have extended constraint handling to predicate logic over larger LLMs: NeuroLogic Decoding (Lu et al., 2021) enables unsupervised generation satisfying complex lexical predicates with beam-search-equivalent runtime, while FUDGE (Yang and Klein, 2021) uses future discriminators to steer generation towards desired attributes without retraining the base model. These approaches collectively represent the principal methods for inference-time constrained generation, but all operate on surface-level or attribute-level constraints rather than semantic, policy-level properties such as answer non-leakage, rubric coverage, or scaffold structure. Critically, none provides a formal proof that all policy constraints will be satisfied — compliance remains a best-effort property of the search. The most recent grammar-constrained decoding work (Geng et al., 2023) has demonstrated tractable structural constraint enforcement for structured NLP tasks such as semantic parsing, but targets structured output formats rather than the open-ended semantic policies required for educational feedback. More recently, practical structured generation frameworks have extended this to schema-driven and regular-expression-driven output control at inference time (Willard and Louf, 2024), confirming the engineering viability of syntax-level enforcement — but these frameworks equally remain restricted to structural output formats and cannot express or verify semantic, policy-level properties such as answer non-leakage or rubric compliance. This proposal addresses that limitation directly through a verifier-in-the-loop decoding design with formal correctness arguments, extending the line of work initiated by Lu et al. (2021) to a semantically richer and formally verifiable constraint regime — the key distinction being that VCD targets policy semantics rather than structural output formats.

Alignment and Multi-Objective Optimisation

The dominant alignment paradigm uses reinforcement learning from human feedback (RLHF) to steer LLM behaviour towards human-preferred outputs (Christiano et al., 2017; Ouyang et al., 2022). Direct Preference Optimisation (DPO) subsequently removed the need for a separate reward model, improving training stability (Rafailov et al., 2023). Both approaches optimise a single aggregate reward, which is a fundamental limitation when objectives such as pedagogical utility, constraint compliance, and equity cannot be reduced to a single scalar without significant information loss. Constrained Markov Decision Processes (Altman, 1999) and constrained policy optimisation (Achiam et al., 2017) provide theoretical frameworks for multi-objective problems under explicit constraints, but have not been applied to LLM alignment in educational contexts. This proposal bridges that gap by building on DPO’s training efficiency while incorporating a multi-objective formulation with Pareto analysis.

Evaluation Methods

Automatic evaluation metrics for generated text are widely acknowledged to be poorly correlated with human judgements of quality, particularly for open-ended generation tasks. Comparative judgement offers a principled alternative: rather than rating outputs in isolation, evaluators judge pairs, and a ranking is recovered via models with well-understood reliability properties (Thurstone, 1927; Bradley and Terry, 1952; Kendall and Babington Smith, 1939). Meta-analytic evidence confirms that comparative judgement produces highly reliable rankings across open-ended assessment tasks including essay marking (Verhavert et al., 2019), yet the methodology has not been systematically applied to AI-generated feedback. The CJ-Bench benchmark proposed here extends this methodology to that domain, providing a reusable, human-grounded evaluation protocol with explicit inter-rater reliability targets.

Pedagogical Theory Foundations

The policy constraints and evaluation criteria in this proposal are grounded in established educational theory rather than derived solely from engineering intuition. Formative assessment theory (Black and Wiliam, 1998) identifies feedback as the central mechanism by which learners close the gap between current and target performance; it emphasises the importance of feedback that is actionable, timely, and calibrated to the learner’s state — properties that directly motivate the rubric-alignment and scaffold-structure constraints in the PCG framework. Vygotsky’s concept of the Zone of Proximal Development (ZPD) and the related construct of scaffolding (Vygotsky, 1978) provide the theoretical basis for hint-depth regulation: effective scaffolded support operates just beyond a learner’s independent capability and is progressively withdrawn as competence develops, which is precisely the behaviour that non-leakage and scaffold-structure constraints are designed to enforce. Hattie and Timperley’s (2007) model of feedback identifies four levels — task, process, self-regulation, and self — and demonstrates that process-level feedback consistently produces the strongest learning gains; this model informs the design of the CJ-Bench evaluation rubric and the utility component of the MOA-Edu objective. Together, these theoretical anchors ground the policy language in academic theory and provide an independent basis for interpreting empirical findings beyond technical performance metrics.

AI in Education Context

Systematic reviews confirm rapid growth of AI applications in higher education but identify persistent concerns about pedagogical quality, ethics, and rigour (Bond et al., 2024), with specific evidence of uneven implementation readiness and equity challenges in STEM contexts (Manorat et al., 2025; Apata et al., 2025). Related work within the supervisory group has explored compact LLM fine-tuning for educational video generation, demonstrating feasibility of resource-efficient LLM deployment in educational settings. Fairness in recommendation and evaluation systems (Ekstrand et al., 2022) provides methodological grounding for the equity analysis planned in CJ-Bench.

Collectively, this body of work establishes that constrained decoding is feasible but incompletely understood in terms of correctness guarantees; multi-objective alignment is theoretically grounded but unapplied to education; comparative judgement is reliable but unapplied to AI feedback; and AI-in-education is growing but under-evaluated by rigorous human-grounded standards. This proposal addresses all four gaps in a single coherent research programme. A PRISMA 2020-compliant systematic review at the outset of the programme will provide a rigorous, independently verifiable mapping of these gaps before the technical work commences.

Research Question and Objectives

Primary research question: Whether and to what extent can large language models be designed and aligned to deliver safe, pedagogy-aligned formative feedback with verifiable constraint compliance, strong learning utility, and fair outcomes across student groups?

Objectives:

0. Conduct a PRISMA 2020 systematic literature review to map the current state of knowledge in constrained LLM generation, multi-objective alignment, and AI-generated educational feedback evaluation, and to derive precise research questions grounded in identified knowledge gaps.
1. Design a formal Pedagogy-Constrained Generation (PCG) framework — including a domain-specific policy language and verifier — to investigate how non-leakage, rubric alignment, and scaffolded feedback structure can be expressed as computable constraints, grounded in formative assessment theory and Vygotskian scaffolding principles.
2. Design and analyse a novel verifier-guided constrained decoding algorithm (VCD), investigating its correctness properties under stated assumptions and characterising its time and space complexity.
3. Build a Multi-Objective Alignment pipeline (MOA-Edu) — a DPO variant jointly optimising pedagogical quality, compliance, and fairness — and map trade-offs using Pareto analysis.
4. Create and release CJ-Bench, a human-grounded benchmark of authentic programming and mathematics artefacts with blind comparative judgement protocols and reliability analysis, exploring what levels of agreement and reliability are achievable and meaningful in this context.
5. Validate the full system against strong baselines, using the research itself to explore and characterise what constitutes meaningful performance on metrics including verifier compliance rate, comparative judgement agreement, equity impact, and utility — and assess predictive links to learning outcomes where feasible.

Formal Problem Statement

Let x ∈ 𝒳 denote a student artefact and context tuple (submission, rubric, task metadata, learner state), and let y = (y₁,…,y_T) be generated feedback tokens over vocabulary 𝒱. Let Π be a finite set of pedagogical policies (for example, non-leakage, scaffold structure, rubric coverage) and let V(y,x,Π) ∈ {0, 1} be a verifier that returns 1 if all active constraints are satisfied.

Inputs: 1. A base language model p_θ(y∣x). 2. Policy specification Π and verifier V. 3. Preference/evaluation signals for utility and fairness.

Constraint set: 𝒴_Π(x) = {y : V(y,x,Π) = 1}.

Decoding objective: y^* = arg max_{y ∈ 𝒴Π(x)} S_θ(y∣x), where S_θ is the sequence score induced by the model and decoding strategy.

Multi-objective alignment objective: max_θ 𝔼_(x,y)[λ_uU(y,x)+λ_cC(y,x)+λ_fF(y,x)], with utility U, compliance C, fairness F, and trade-off weights λ_u, λ_c, λ_f ≥ 0.

Formal investigation targets: 1. Correctness: investigate whether, and under what grammatical and policy assumptions, the proposed VCD algorithm can be shown to return outputs in 𝒴_Π(x) when a feasible completion exists. 2. Complexity: characterise worst-case bounds for VCD runtime and memory as functions of beam width, sequence length, verifier cost, and grammar/policy size. 3. Approximation/utility trade-off: explore the extent to which utility is preserved relative to unconstrained decoding under the same model and search budget, and characterise conditions under which the trade-off is acceptable.

Methodology and Research Design

This project employs a mixed-methods design combining systematic review, formal and theoretical work, empirical quantitative experimentation, and human-panel evaluation. The four strands correspond to the four core phases of the programme and are delivered in sequence, with the systematic review providing the evidentiary foundation for all subsequent work.

Strand 0 — Systematic Literature Review (SR). A PRISMA 2020-compliant systematic review will be conducted across three intersecting fields: constrained LLM generation, multi-objective alignment, and AI-generated educational feedback evaluation. Search strings, inclusion/exclusion criteria, screening decisions, and PRISMA flow diagrams will be fully documented. This strand serves two purposes: (1) to provide a rigorous, independently verifiable mapping of knowledge gaps that grounds the research questions derived in Strands 1–3; and (2) to produce the first standalone publication of the programme. The review will be conducted during M1–9 alongside ethics application submission and baseline infrastructure setup. Formative assessment theory, scaffolding theory, and Hattie and Timperley’s feedback model will be included as a fourth domain in the review scope to ensure the technical contributions are anchored in the pedagogical literature.

Strand 1 — Formal methods and algorithm design (C1/VCD). A context-free grammar-based policy language will be specified to express feedback constraints (hint depth, leakage prohibition, rubric coverage), grounded in the formative assessment and scaffolding frameworks identified in the SR. A verifier V will be implemented over this grammar. The VCD algorithm will be designed and formally analysed: correctness will be investigated with respect to the grammar semantics under stated assumptions, and worst-case time and space complexity will be characterised as functions of key parameters. This strand requires no participant data. Grammar-guided decoding is chosen over post-hoc filtering because it provides structural completeness properties — the decoder cannot produce a non-compliant output if the grammar is correctly specified — a property that filtering cannot match.

Strand 2 — Multi-objective alignment (C2/MOA-Edu). Fine-tuning will proceed on open-weight models (initially sub-10B parameter for compute efficiency) using a DPO-variant loss extended to three objectives. DPO is chosen over full RLHF because it eliminates the reward model, reducing training instability and compute overhead. Pareto surfaces will be mapped by varying objective weights (λ_u,λ_c,λ_f) across a grid. Quantisation-aware deployment will maintain feasibility on accessible compute (Frantar et al., 2023). Ablations will isolate the contribution of each objective term.

Strand 3 — Human-grounded evaluation (C3/CJ-Bench). Authentic student programming and mathematics submissions will be collected from NTU and a partner institution, subject to institutional agreement and ethics approval obtained in M1–6. All data will be collected with informed consent and anonymised prior to use. Panels of STEM educators and practitioners will evaluate AI-generated feedback in blind pairwise comparative judgement trials. Panel sizing will follow reliability guidelines of Bradley and Terry (1952). CJ is chosen over direct rating because it recovers a more reliable rank order from fewer judgements and is less susceptible to rater scale-use differences than Likert scoring. A technology acceptance study with colleagues as subjects will complement the CJ panels, contributing to the characterisation of what makes AI feedback acceptable to practitioners and providing additional data for the ethics-approved human participant strand.

Feasibility is supported by a phased 60-month plan calibrated to part-time study, that limits participant recruitment to Strand 3, uses accessible open-weight models throughout, and scopes the formal analysis to a tractable grammar class. Risk controls for data access, compute constraints, and panel recruitment are described in the Risk and Mitigation section.

Evaluation Plan

• Datasets: CJ-Bench v1 (programming), CJ-Bench v2 (mathematics).
• Systems compared: VCD+PCG+MOA-Edu, prompt-only, post-hoc filters, grammar-only decoding, single-objective RLHF, and vanilla RAG.
• Protocols: cross-domain generalisation, unseen tasks, and adversarial leakage prompts.
• Metrics: CJ-Agreement, Verifier Pass Rate, Equity Impact, Utility, and Latency/Throughput.
• Analysis: confidence intervals, bootstrap, significance testing, Pareto surfaces, and effect sizes.

Timeline and Delivery Plan (60 months, Part-Time)

The timeline is designed for part-time doctoral study. Ethics applications and the systematic review run concurrently in the first phase, ensuring that data-dependent strands are not blocked.

• M1–9: Ethics applications submitted at M1 (NTU and partner institution in parallel). PRISMA 2020 systematic literature review (Strand 0): search, screening, synthesis. Baseline infrastructure and pilot CJ task design. Publication target: PRISMA review submitted to journal by M9.
• M10–18: DSL and verifier design (Strand 1). VCD algorithm design and initial correctness investigation. Complexity characterisation. Pilot VCD implementation. Publication target: workshop or short paper on VCD design by M18.
• M19–30: Full VCD implementation and empirical evaluation. CJ-Bench v1 (programming) — ethics-approved data collection. CJ panel trials (programming domain). Publication target: conference paper on VCD+PCG by M30.
• M31–42: MOA-Edu training and ablations (Strand 2). Integration with VCD+PCG. Pareto surface analysis. Technology acceptance study. Publication target: conference or journal paper on MOA-Edu by M42.
• M43–54: Expanded cross-domain evaluation. Fairness and equity analysis. CJ-Bench v2 (mathematics). Predictive validity checks. Library hardening and leaderboard release. Publication target: CJ-Bench paper and equity analysis by M54.
• M55–60: Thesis writing, final submission, viva preparation.

Outputs and Deliverables

• PRISMA 2020 systematic literature review (journal publication).
• VCD algorithm specification with correctness investigation and complexity characterisation.
• PCG library (grammar, verifier, decoding) with documentation.
• MOA-Edu pipeline.
• CJ-Bench v1 and v2 datasets and leaderboard artefacts.
• Technology acceptance study report.
• Four publications or equivalent outputs across methods, evaluation, and education venues (see Publication Plan below).

Publication Plan

Ethics and Research Governance

Ethics approval is a first-order task, not a background administrative matter, and is treated accordingly in the timeline. Ethics applications to NTU and the partner institution will be submitted at M1, in parallel, to ensure that data collection for Strand 3 is not delayed. The PRISMA review (M1–9) and Strand 1 formal methods work (M10–18) require no participant data, providing a productive period during which ethics approval is obtained before any data-dependent work commences.

This project involves two categories of human participant activity. First, panels of STEM educators and practitioners will participate in comparative judgement trials evaluating AI-generated feedback; informed consent will be obtained, participation will be voluntary, and data will be anonymised and stored in accordance with UK GDPR. Second, a technology acceptance study will involve colleagues as subjects; this will require a separate ethics sub-application covering that activity specifically. Authentic student artefacts will be anonymised prior to use. Cross-institutional data sharing will be governed by a formal data-sharing agreement between NTU and the partner institution. All participant data will be stored on NTU-approved secure infrastructure and deleted in accordance with the approved data retention schedule.

Risk and Mitigation

• Part-time timeline: The 60-month schedule is calibrated for part-time study, but dependency chains between strands mean that delays in ethics approval or data access could compress the later strands. Mitigation: ethics applications are initiated at M1; Strand 0 (literature review) and Strand 1 (formal methods) require no participant data and can progress in full during the approval period.
• Data ethics and access: Opt-in collection and anonymisation; cross-institutional data access requires parallel ethics applications at both institutions, initiated at M1. A data-sharing agreement will be drafted at the same time.
• Verifier latency: Running the verifier at each decoding step adds computational overhead; managed through grammar optimisation, caching of verifier states, and early-termination heuristics, with latency benchmarked explicitly against unconstrained baselines.
• Compliance vs utility trade-offs: Adaptive weighting and repair mechanisms; the Pareto analysis is designed specifically to characterise this trade-off empirically rather than assume it is negligible.
• Panel variability and recruitment: Panel sizing follows Bradley and Terry (1952) reliability guidelines; recruitment through NTU and partner institution networks; technology acceptance study with colleagues provides a more accessible supplementary cohort.
• Scope creep: Strands 0–3 are the core deliverables; evaluation scope will be controlled through predefined protocols and fixed benchmark designs agreed with the supervisory team at the start of each strand.
• Compute access: Sub-10B open-weight models with quantisation (Frantar et al., 2023) are used throughout; cloud compute supplementation is available if local infrastructure is constrained.

Supervisory Team

• Director of Studies: Dr Jordan Bird, Nottingham Trent University
• Supervisor: Dr Isibor Kennedy Ihianle, Nottingham Trent University
• Supervisor: Dr Golnaz Shahtahmassebi, Nottingham Trent University

Expected Contribution and Impact

• A novel constrained decoding algorithm with provable bounds for safe and controllable text generation.
• Generalisable methods for policy-aware alignment under competing objectives.
• Reusable infrastructure for human-grounded evaluation.
• Practical impact on educational feedback quality, transparency, and equity.

NTU Competency Evidence

This project is designed to evidence NTU competency areas directly.

• Analytical thinking: formal specification, proof-oriented reasoning, and rigorous comparative evaluation.
• Planning: a structured 36-month workplan with milestones, deliverables, and explicit success criteria.
• Communication: publication-ready writing, technical documentation, and explanation for specialist and non-specialist audiences.
• Resilience: proactive risk management, contingency pathways for data/compute constraints, and iterative refinement after pilot results.
• Independence: ownership of method design, implementation, and evaluation from problem definition to validated outputs.
• Collaboration: supervisory engagement, comparative judgement panel design, and interdisciplinary work with educational and technical stakeholders.

NTU is the natural home for this work: Dr Jordan Bird’s research group holds direct expertise in LLM applications for education, and the supervisory team spans NLP, educational technology, and AI safety — precisely the combination required by this project’s three strands.

Acceptance Criteria

Rather than pre-specifying fixed performance thresholds, part of the research contribution is to characterise what constitutes meaningful performance in each domain. The following framing reflects this exploratory intent:

• VCD+PCG: A formal algorithm specification with a correctness investigation under stated assumptions and an explicit characterisation of time and space complexity. Empirically, the research will explore the range of verifier compliance rates achievable under different grammar designs and beam configurations, and investigate what compliance-utility trade-off profiles are acceptable to practitioners.
• MOA-Edu: Demonstration of Pareto-efficient policies that improve at least one objective without degrading another relative to single-objective alignment baselines. The research will characterise the shape of the Pareto frontier across the three objectives.
• CJ-Bench: A reliable, reusable benchmark with inter-rater reliability reported and contextualised against the comparative judgement literature. The research will investigate what reliability levels are achievable and meaningful for this specific evaluation task, including through the technology acceptance study.

All criteria are subject to refinement in collaboration with the supervisory team following the systematic review findings.

Conclusion

This proposal presents a coherent, academically rigorous research programme investigating three interconnected areas: constrained text generation, multi-objective alignment, and human-grounded evaluation. The central contribution — an investigation of whether and under what conditions a verifier-guided constrained decoding algorithm can be shown to have correctness properties and characterisable complexity — represents a substantive and original addition to the CS literature that extends beyond its educational application. The multi-objective alignment pipeline and CJ-Bench benchmark provide complementary theoretical and empirical contributions with clear generalisability. The project is designed to be feasible within a part-time doctoral timescale of 60 months, grounded in a strong body of prior work, and structured to produce outputs of value to the academic community, educators, and practitioners. The PRISMA systematic review at the outset ensures that research questions are derived from a rigorous, independently verifiable mapping of the field, and the publication plan provides a structured progression from review to algorithm to alignment to benchmark. It directly addresses an urgent, real-world problem — the lack of trustworthy, verifiable AI feedback in STEM education — with methods rigorous enough to withstand peer review and practical enough to be evaluated in authentic settings.

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