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Brandon Fain

Publications and source records attributed to Brandon Fain.

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Reflect: Transparent Principle-Guided Reasoning for Constitutional Alignment at Scale

The constitutional framework of alignment aims to align large language models (LLMs) with value-laden principles written in natural language (such as to avoid using biased language). Prior work has focused on parameter fine-tuning techniques, such as reinforcement learning from human feedback (RLHF), to instill these principles. However, these approaches are computationally demanding, require careful engineering and tuning, and often require difficult-to-obtain human annotation data. We propose \textsc{reflect}, an inference-time framework for constitutional alignment that does not require any training or data, providing a plug-and-play approach for aligning an instruction-tuned model to a set of principles. \textsc{reflect} operates entirely in-context, combining a (i) constitution-conditioned base response with post-generation (ii) self-evaluation, (iii)(a) self-critique, and (iii)(b) final revision. \textsc{reflect}'s technique of explicit in-context reasoning over principles during post-generation outperforms standard few-shot prompting and provides transparent reasoning traces. Our results demonstrate that \textsc{reflect} significantly improves LLM conformance to diverse and complex principles, including principles quite distinct from those emphasized in the model's original parameter fine-tuning, without sacrificing factual reasoning. \textsc{reflect} is particularly effective at reducing the rate of rare but significant violations of principles, thereby improving safety and robustness in the tail end of the distribution of generations. Finally, we show that \textsc{reflect} naturally generates useful training data for traditional parameter fine-tuning techniques, allowing for efficient scaling and the reduction of inference-time computational overhead in long-term deployment scenarios.

cs.CL

Beyond Preferences: Learning Alignment Principles Grounded in Human Reasons and Values

A crucial consideration when developing and deploying Large Language Models (LLMs) is the human values to which these models are aligned. In the constitutional framework of alignment models are aligned to a set of principles (the constitution) specified in natural language. However, it is unclear how to fairly determine this constitution with widespread stakeholder input. In this work we propose Grounded Constitutional AI (GCAI), a unified framework for generating constitutions of principles that are representative of both users' general expectations toward AI (general principles) and their interaction-time preferences (contextual principles). We extend the Inverse Constitutional AI (ICAI) approach to generate contextual principles from human preference annotation data by leveraging human-provided \textit{reasons} for their preferences. We supplement these contextual principles with general principles surfaced from user statements of \textit{values} regarding AI. We show that a constitution generated by GCAI is preferred by humans over one generated through ICAI both personally, and for widespread use in governing AI behavior. Additionally participants consider the GCAI constitution to be more morally grounded, coherent, and pluralistic.

cs.LG

Multi-objective Reinforcement Learning with Nonlinear Preferences: Provable Approximation for Maximizing Expected Scalarized Return

We study multi-objective reinforcement learning with nonlinear preferences over trajectories. That is, we maximize the expected value of a nonlinear function over accumulated rewards (expected scalarized return or ESR) in a multi-objective Markov Decision Process (MOMDP). We derive an extended form of Bellman optimality for nonlinear optimization that explicitly considers time and current accumulated reward. Using this formulation, we describe an approximation algorithm for computing an approximately optimal non-stationary policy in pseudopolynomial time for smooth scalarization functions with a constant number of rewards. We prove the approximation analytically and demonstrate the algorithm experimentally, showing that there can be a substantial gap between the optimal policy computed by our algorithm and alternative baselines.

cs.LG

Do Not Harm Protected Groups in Debiasing Language Representation Models

Language Representation Models (LRMs) trained with real-world data may capture and exacerbate undesired bias and cause unfair treatment of people in various demographic groups. Several techniques have been investigated for applying interventions to LRMs to remove bias in benchmark evaluations on, for example, word embeddings. However, the negative side effects of debiasing interventions are usually not revealed in the downstream tasks. We propose xGAP-DEBIAS, a set of evaluations on assessing the fairness of debiasing. In this work, We examine four debiasing techniques on a real-world text classification task and show that reducing biasing is at the cost of degrading performance for all demographic groups, including those the debiasing techniques aim to protect. We advocate that a debiasing technique should have good downstream performance with the constraint of ensuring no harm to the protected group.

cs.CL

Fairness in the Assignment Problem with Uncertain Priorities

In the assignment problem, a set of items must be allocated to unit-demand agents who express ordinal preferences (rankings) over the items. In the assignment problem with priorities, agents with higher priority are entitled to their preferred goods with respect to lower priority agents. A priority can be naturally represented as a ranking and an uncertain priority as a distribution over rankings. For example, this models the problem of assigning student applicants to university seats or job applicants to job openings when the admitting body is uncertain about the true priority over applicants. This uncertainty can express the possibility of bias in the generation of the priority ranking. We believe we are the first to explicitly formulate and study the assignment problem with uncertain priorities. We introduce two natural notions of fairness in this problem: stochastic envy-freeness (SEF) and likelihood envy-freeness (LEF). We show that SEF and LEF are incompatible and that LEF is incompatible with ordinal efficiency. We describe two algorithms, Cycle Elimination (CE) and Unit-Time Eating (UTE) that satisfy ordinal efficiency (a form of ex-ante Pareto optimality) and SEF; the well known random serial dictatorship algorithm satisfies LEF and the weaker efficiency guarantee of ex-post Pareto optimality. We also show that CE satisfies a relaxation of LEF that we term 1-LEF which applies only to certain comparisons of priority, while UTE satisfies a version of proportional allocations with ranks. We conclude by demonstrating how a mediator can model a problem of school admission in the face of bias as an assignment problem with uncertain priority.

cs.GT

Multi-Analyst Differential Privacy for Online Query Answering

Most differentially private mechanisms are designed for the use of a single analyst. In reality, however, there are often multiple stakeholders with different and possibly conflicting priorities that must share the same privacy loss budget. This motivates the problem of equitable budget-sharing for multi-analyst differential privacy. Our previous work defined desiderata that any mechanism in this space should satisfy and introduced methods for budget-sharing in the offline case where queries are known in advance. We extend our previous work on multi-analyst differentially private query answering to the case of online query answering, where queries come in one at a time and must be answered without knowledge of the following queries. We demonstrate that the unknown ordering of queries in the online case results in a fundamental limit in the number of queries that can be answered while satisfying the desiderata. In response, we develop two mechanisms, one which satisfies the desiderata in all cases but is subject to the fundamental limitations, and another that randomizes the input order ensuring that existing online query answering mechanisms can satisfy the desiderata.

cs.CY

Welfare and Fairness in Multi-objective Reinforcement Learning

We study fair multi-objective reinforcement learning in which an agent must learn a policy that simultaneously achieves high reward on multiple dimensions of a vector-valued reward. Motivated by the fair resource allocation literature, we model this as an expected welfare maximization problem, for some nonlinear fair welfare function of the vector of long-term cumulative rewards. One canonical example of such a function is the Nash Social Welfare, or geometric mean, the log transform of which is also known as the Proportional Fairness objective. We show that even approximately optimal optimization of the expected Nash Social Welfare is computationally intractable even in the tabular case. Nevertheless, we provide a novel adaptation of Q-learning that combines nonlinear scalarized learning updates and non-stationary action selection to learn effective policies for optimizing nonlinear welfare functions. We show that our algorithm is provably convergent, and we demonstrate experimentally that our approach outperforms techniques based on linear scalarization, mixtures of optimal linear scalarizations, or stationary action selection for the Nash Social Welfare Objective.

cs.GT

Centrality with Diversity

Graph centrality measures use the structure of a network to quantify central or "important" nodes, with applications in web search, social media analysis, and graphical data mining generally. Traditional centrality measures such as the well known PageRank interpret a directed edge as a vote in favor of the importance of the linked node. We study the case where nodes may belong to diverse communities or interests and investigate centrality measures that can identify nodes that are simultaneously important to many such diverse communities. We propose a family of diverse centrality measures formed as fixed point solutions to a generalized nonlinear eigenvalue problem. Our measure can be efficiently computed on large graphs by iterated best response and we study its normative properties on both random graph models and real-world data. We find that we are consistently and efficiently able to identify the most important diverse nodes of a graph, that is, those that are simultaneously central to multiple communities.

cs.SI

Budget Sharing for Multi-Analyst Differential Privacy

Large organizations that collect data about populations (like the US Census Bureau) release summary statistics that are used by multiple stakeholders for resource allocation and policy making problems. These organizations are also legally required to protect the privacy of individuals from whom they collect data. Differential Privacy (DP) provides a solution to release useful summary data while preserving privacy. Most DP mechanisms are designed to answer a single set of queries. In reality, there are often multiple stakeholders that use a given data release and have overlapping but not-identical queries. This introduces a novel joint optimization problem in DP where the privacy budget must be shared among different analysts. We initiate study into the problem of DP query answering across multiple analysts. To capture the competing goals and priorities of multiple analysts, we formulate three desiderata that any mechanism should satisfy in this setting -- The Sharing Incentive, Non-Interference, and Adaptivity -- while still optimizing for overall error. We demonstrate how existing DP query answering mechanisms in the multi-analyst settings fail to satisfy at least one of the desiderata. We present novel DP algorithms that provably satisfy all our desiderata and empirically show that they incur low error on realistic tasks.

cs.DB

Concentration of Distortion: The Value of Extra Voters in Randomized Social Choice

We study higher statistical moments of Distortion for randomized social choice in a metric implicit utilitarian model. The Distortion of a social choice mechanism is the expected approximation factor with respect to the optimal utilitarian social cost (OPT). The $k^{th}$ moment of Distortion is the expected approximation factor with respect to the $k^{th}$ power of OPT. We consider mechanisms that elicit alternatives by randomly sampling voters for their favorite alternative. We design two families of mechanisms that provide constant (with respect to the number of voters and alternatives) $k^{th}$ moment of Distortion using just $k$ samples if all voters can then participate in a vote among the proposed alternatives, or $2k-1$ samples if only the sampled voters can participate. We also show that these numbers of samples are tight. Such mechanisms deviate from a constant approximation to OPT with probability that drops exponentially in the number of samples, independent of the total number of voters and alternatives. We conclude with simulations on real-world Participatory Budgeting data to qualitatively complement our theoretical insights.

cs.GT

Proportionally Fair Clustering

We extend the fair machine learning literature by considering the problem of proportional centroid clustering in a metric context. For clustering $n$ points with $k$ centers, we define fairness as proportionality to mean that any $n/k$ points are entitled to form their own cluster if there is another center that is closer in distance for all $n/k$ points. We seek clustering solutions to which there are no such justified complaints from any subsets of agents, without assuming any a priori notion of protected subsets. We present and analyze algorithms to efficiently compute, optimize, and audit proportional solutions. We conclude with an empirical examination of the tradeoff between proportional solutions and the $k$-means objective.

cs.LG

Random Dictators with a Random Referee: Constant Sample Complexity Mechanisms for Social Choice

We study social choice mechanisms in an implicit utilitarian framework with a metric constraint, where the goal is to minimize \textit{Distortion}, the worst case social cost of an ordinal mechanism relative to underlying cardinal utilities. We consider two additional desiderata: Constant sample complexity and Squared Distortion. Constant sample complexity means that the mechanism (potentially randomized) only uses a constant number of ordinal queries regardless of the number of voters and alternatives. Squared Distortion is a measure of variance of the Distortion of a randomized mechanism. Our primary contribution is the first social choice mechanism with constant sample complexity \textit{and} constant Squared Distortion (which also implies constant Distortion). We call the mechanism Random Referee, because it uses a random agent to compare two alternatives that are the favorites of two other random agents. We prove that the use of a comparison query is necessary: no mechanism that only elicits the top-k preferred alternatives of voters (for constant k) can have Squared Distortion that is sublinear in the number of alternatives. We also prove that unlike any top-k only mechanism, the Distortion of Random Referee meaningfully improves on benign metric spaces, using the Euclidean plane as a canonical example. Finally, among top-1 only mechanisms, we introduce Random Oligarchy. The mechanism asks just 3 queries and is essentially optimal among the class of such mechanisms with respect to Distortion. In summary, we demonstrate the surprising power of constant sample complexity mechanisms generally, and just three random voters in particular, to provide some of the best known results in the implicit utilitarian framework.

cs.GT

Fair Allocation of Indivisible Public Goods

We consider the problem of fairly allocating indivisible public goods. We model the public goods as elements with feasibility constraints on what subsets of elements can be chosen, and assume that agents have additive utilities across elements. Our model generalizes existing frameworks such as fair public decision making and participatory budgeting. We study a groupwise fairness notion called the core, which generalizes well-studied notions of proportionality and Pareto efficiency, and requires that each subset of agents must receive an outcome that is fair relative to its size. In contrast to the case of divisible public goods (where fractional allocations are permitted), the core is not guaranteed to exist when allocating indivisible public goods. Our primary contributions are the notion of an additive approximation to the core (with a tiny multiplicative loss), and polynomial time algorithms that achieve a small additive approximation, where the additive factor is relative to the largest utility of an agent for an element. If the feasibility constraints define a matroid, we show an additive approximation of 2. A similar approach yields a constant additive bound when the feasibility constraints define a matching. More generally, if the feasibility constraints define an arbitrary packing polytope with mild restrictions, we show an additive guarantee that is logarithmic in the width of the polytope. Our algorithms are based on variants of the convex program for maximizing the Nash social welfare, but differ significantly from previous work in how it is used. Our guarantees are meaningful even when there are fewer elements than the number of agents. As far as we are aware, our work is the first to approximate the core in indivisible settings.

cs.GT

Sequential Deliberation for Social Choice

In large scale collective decision making, social choice is a normative study of how one ought to design a protocol for reaching consensus. However, in instances where the underlying decision space is too large or complex for ordinal voting, standard voting methods of social choice may be impractical. How then can we design a mechanism - preferably decentralized, simple, scalable, and not requiring any special knowledge of the decision space - to reach consensus? We propose sequential deliberation as a natural solution to this problem. In this iterative method, successive pairs of agents bargain over the decision space using the previous decision as a disagreement alternative. We describe the general method and analyze the quality of its outcome when the space of preferences define a median graph. We show that sequential deliberation finds a 1.208- approximation to the optimal social cost on such graphs, coming very close to this value with only a small constant number of agents sampled from the population. We also show lower bounds on simpler classes of mechanisms to justify our design choices. We further show that sequential deliberation is ex-post Pareto efficient and has truthful reporting as an equilibrium of the induced extensive form game. We finally show that for general metric spaces, the second moment of of the distribution of social cost of the outcomes produced by sequential deliberation is also bounded.

cs.GT

The Core of the Participatory Budgeting Problem

In participatory budgeting, communities collectively decide on the allocation of public tax dollars for local public projects. In this work, we consider the question of fairly aggregating the preferences of community members to determine an allocation of funds to projects. This problem is different from standard fair resource allocation because of public goods: The allocated goods benefit all users simultaneously. Fairness is crucial in participatory decision making, since generating equitable outcomes is an important goal of these processes. We argue that the classic game theoretic notion of core captures fairness in the setting. To compute the core, we first develop a novel characterization of a public goods market equilibrium called the Lindahl equilibrium, which is always a core solution. We then provide the first (to our knowledge) polynomial time algorithm for computing such an equilibrium for a broad set of utility functions; our algorithm also generalizes (in a non-trivial way) the well-known concept of proportional fairness. We use our theoretical insights to perform experiments on real participatory budgeting voting data. We empirically show that the core can be efficiently computed for utility functions that naturally model our practical setting, and examine the relation of the core with the familiar welfare objective. Finally, we address concerns of incentives and mechanism design by developing a randomized approximately dominant-strategy truthful mechanism building on the exponential mechanism from differential privacy.

cs.GT

ROBUS: Fair Cache Allocation for Multi-tenant Data-parallel Workloads

Systems for processing big data---e.g., Hadoop, Spark, and massively parallel databases---need to run workloads on behalf of multiple tenants simultaneously. The abundant disk-based storage in these systems is usually complemented by a smaller, but much faster, {\em cache}. Cache is a precious resource: Tenants who get to use cache can see two orders of magnitude performance improvement. Cache is also a limited and hence shared resource: Unlike a resource like a CPU core which can be used by only one tenant at a time, a cached data item can be accessed by multiple tenants at the same time. Cache, therefore, has to be shared by a multi-tenancy-aware policy across tenants, each having a unique set of priorities and workload characteristics. In this paper, we develop cache allocation strategies that speed up the overall workload while being {\em fair} to each tenant. We build a novel fairness model targeted at the shared resource setting that incorporates not only the more standard concepts of Pareto-efficiency and sharing incentive, but also define envy freeness via the notion of {\em core} from cooperative game theory. Our cache management platform, ROBUS, uses randomization over small time batches, and we develop a proportionally fair allocation mechanism that satisfies the core property in expectation. We show that this algorithm and related fair algorithms can be approximated to arbitrary precision in polynomial time. We evaluate these algorithms on a ROBUS prototype implemented on Spark with RDD store used as cache. Our evaluation on a synthetically generated industry-standard workload shows that our algorithms provide a speedup close to performance optimal algorithms while guaranteeing fairness across tenants.

cs.DC