15-281, Fall 2023

Artificial Intelligence: Representation and Problem Solving


Key Information

Tuesday + Thursday, 11:00am - 12:20pm, DH 2210

Friday afternoon, see Recitations

see the 281 Staff page

Grades will be collected in Canvas.
Midterms 15% (each), Final 30%, Programming homework 20%, Written homework 10%, Online homework 5%, Participation 5%

We will use Piazza for questions and any course announcements.

Students will turn in their homework electronically using Gradescope.

This course is about the theory and practice of Artificial Intelligence. We will study modern techniques for computers to represent task-relevant information and make intelligent (i.e., satisficing or optimal) decisions towards the achievement of goals. The search and problem-solving methods are applicable throughout a large range of industrial, civil, medical, financial, robotic, and information systems. We will investigate questions about AI systems such as: how to represent knowledge, how to effectively generate appropriate sequences of actions and how to search among alternatives to find optimal or near-optimal solutions. We will also explore how to deal with uncertainty in the world and how to learn from experience. We will cover the aggregation of conflicting preferences and computational game theory. Throughout the course, we will discuss topics such as AI and Ethics and introduce applications related to AI for Social Good. We expect that by the end of the course students will have a thorough understanding of the algorithmic foundations of AI, how probability and AI are closely interrelated, and how automated agents make decisions. We also expect students to acquire a strong appreciation of the big-picture aspects of developing fully autonomous intelligent agents.


This 15-281 course is for undergraduates. There is no masters level version offered this semester (15-681).

15-281 used to be 15-381 in previous semesters. This is not a significant change to the course, but rather a recognition that many students are able to complete the necessary prerequisites and are prepared to take this course in their second year.

Prerequisites + Corequisites

The prequisites for this course are:

  • 15-122 Principles of Imperative Computation
  • 21-241 Matrices and Linear Transformations
  • 21-127 Concepts of Mathematics or 15-151 Mathematical Foundations of Computer Science.

The corequisite for this course is:

  • 21-122 Integration and Approximation

For this corequisite, you should either have completed it prior to starting 15-281 or have it on your schedule for Fall 2023.

Please see the instructors if you are unsure whether your background is suitable for the course.

Office Hours

This course uses the CMU OHQueue tool as a queueing system for office hours.

The calendar of in-person and online office hours is below.

Lecture Schedule (subject to change)

Dates Topic Reading / Demo Slides Activity
8/29 Tue Introduction/Agents AIMA Ch. 1 pdf blank/sol
8/31 Thu Search AIMA Ch. 3.1-4 blank pdf
inked pdf
9/5 Tue Informed Search AIMA Ch. 3.5-6 blank pdf
inked pdf
9/7 Thu Adversarial Search AIMA Ch. 5.2-5 blank pdf
inked pdf
9/12 Tue Constraint Satisfaction Problems AIMA Ch. 6.1-3, 6.5
CSP Demo
blank pdf
inked pdf
CSP activity sheet
9/14 Thu Local Search AIMA Ch. 4.1, 6.4 blank pdf
inked pdf
9/19 Tue Optimization & Linear Programming Boyd and Vandenberghe
Ch. 2.2.1, 2.2.4, 4.3-4.3.1
blank pdf
inked pdf
9/21 Thu Integer Programming blank pdf
inked pdf
9/26 Tue Practice Activity and Ethics 1 activity slides: blank pdf
ethics slides: blank pdf
9/28 Thu MIDTERM 1 EXAM In class
10/3 Tue Propositional Logic and Logical Agents AIMA Ch. 7.1-7 blank pdf
inked pdf
10/5 Thu Classical Planning AIMA Ch. 10 blank pdf blank/sol
10/10 Tue Markov Decision Process I AIMA Ch. 17.1-3 blank pdf blank
10/12 Thu Markov Decision Process II blank pptx
10/17 Tue No class: Fall Break
10/19 Thu No class: Fall Break
10/24 Tue Reinforcement Learning I AIMA Ch. 21.1-3 blank pptx
10/26 Thu Reinforcement Learning II AIMA Ch. 21.4-5 blank pptx
10/31 Tue Bayes Nets: Representation AIMA Ch. 13.1-5, 14.1-2
Bayes Net Demo (highres)
blank pptx
11/2 Thu Bayes Nets: Independence AIMA Ch. 13.4-5, 14.2, Jordan 2.1 blank pptx
11/7 Tue NO CLASS, GO VOTE!!
11/9 Thu MIDTERM 2 EXAM In class
11/14 Tue Bayes Nets: Inference AIMA Ch. 14.4 blank pptx blank/sol
11/16 Thu Bayes Nets: Sampling AIMA Ch. 14.5
Likelihood Demo, Gibbs Demo
blank pptx blank
11/21 Tue Hidden Markov Models AIMA Ch. 15.2, 15.5 blank pptx/pdf
inked pptx/pdf
11/23 Thu No class: Thanksgiving
11/28 Tue Particle Filter & HMM Applications AIMA Ch. 15.2, 15.6 blank pptx
11/30 Thu Game Theory: Equilibrium AIMA Ch. 17.5 blank pptx/pdf
inked pptx/pdf
12/5 Tue Game Theory: Social Choice AIMA Ch. 17.6 blank pptx/pdf
inked pptx/pdf
12/7 Thu Ethics/AMA


Recitations start the first week of class, Friday, Sep 1. Recitation attendence is recommended to help solidfy weekly course topics. Students frequently say that the recitations are one of the most important aspects of the course. Attendance is taken and counts towards your course participation grade. That being said, the recitation materials published below are required content and are in-scope for midterm and final exams.

Recitation section assignments will be locked-down after the third week. Until then, you may try attending different recitation sections to find the best fit for you. In the case of any over-crowded recitation sections, priority goes to students that are officially registered for that section in S3. The process to select your final recitation assignment will be announced on Piazza as we get closer to Recitation 4.

Time Location Section TAs Resources
Fri, 10:00 - 10:50 am POS 145 A TAs: Gavin and Lily Slides
Fri, 11:00 - 11:50 am DH 1112 B TAs: Alex and Ayush Slides
Fri, 12:00 - 12:50 pm GHC 4211 C TAs: Ethan and Josep Slides
Fri, 1:00 - 1:50 pm BH 235B D TAs: Ihita and Josep Slides
Fri, 2:00 - 2:50 pm POS 145 E TAs: Raashi and Lily Slides
Fri, 3:00 - 3:50 pm GHC 4102 F TAs: Alex and Ihita Slides
Dates Recitation Handout Code
9/1 Fri Recitation 1: Search pdf (solutions) nim.zip
9/8 Fri Recitation 2: Informed and Adversarial Search pdf (solutions)
9/15 Fri Recitation 3: CSPs and Local Search pdf (solutions)
9/22 Fri Recitation 4: LP and IP pdf (solutions) OR-Tools code
9/29 Fri Recitation 5: Probability Review pdf (solutions)
10/6 Fri Recitation 6: Logic and Classical Planning pdf (solutions) crane.py
10/13 Fri Recitation 7: MDPs pdf (solutions)
10/20 Fri No recitation: Break
10/27 Fri Recitation 8: RL pdf (solutions)
11/3 Fri Recitation 9: Bayes Nets pdf (solutions)
11/10 Fri No Recitation 10: (Post-Midterm 2)
11/17 Fri Recitation 11: Bayes Nets 2 pdf (solutions)
11/24 Fri Recitation 12: Thanksgiving pdf (solutions)
12/1 Fri Recitation 13: PF and Game Theory pdf (solutions)
12/8 Fri Recitation 14: Social Choice and Review pdf (solutions)
Final Exam Review pdf (solutions)


The course includes two midterm exams and a final exam. The midterms will be in class on Sep.28 and Nov 9. The final exam date is to-be-determined. Plan any travel around exams, as exams cannot be rescheduled.

Midterm 1 Learning Objectives and Practice Exams

Midterm 2 Learning Objectives and Practice Exams

Final Exam Learning Objectives and Practice Exams


There will be five programming assignments and ten written/online assignments (subject to change). Written/online assignments will involve working through algorithms presented in the class, deriving and proving mathematical results, and critically analyzing material presented in class. Programming assignments will involve writing code in Python to implement various algorithms.

For any assignments that aren't released yet, the dates below are tentative and subject to change.

For helpful information about getting started with our written and programming assignments, visit our FAQ page.

Assignment due dates

Assignment Link (if released) Due Date
P0 P0: Tutorial (required, worth zero points) 9/1 Fri, 10 pm
HW1 (online) Gradescope 9/5 Tue, 10 pm
P1 P1: Search and Games 9/18 Monday, 10 pm
HW2 (written) hw2_blank.pdf, hw2.zip (tex src) 9/12 Tue, 10 pm
HW3 (online) Gradescope 9/19 Tue, 10 pm
P2 P2: Optimization 10/5 Thu, 10 pm
HW4 (online) Gradescope 9/26 Tue, 10 pm
HW5 (written) hw5_blank.pdf, hw5.zip (tex src) 10/10 Tue, 10 pm
P3 Checkpoint (12 points) P3: Logic/Classical Planning 10/13 Fri, 10 pm
HW6 (online) Gradescope 10/24 Tue, 10 pm
P3 Final (25 points) P3: Logic/Classical Planning 10/27 Fri, 10 pm
HW7 (written) hw7_blank.pdf, hw7.zip (tex src) 10/31 Tue, 10 pm
HW8 (online) Gradescope 11/7 Tue, 10 pm
P4 P4: Reinforcement Learning 11/16 Thu, 10 pm
HW9 (written) hw9_blank.pdf, hw9.zip (tex src) 11/21 Tue, 10 pm
HW10 (written) hw10_blank.pdf, hw10.zip (tex src) 12/5 Tue, 10 pm
P5 P5: Ghostbusters 12/7 Thu, 10 pm

Course Notes

Below are course notes developed by the course staff over the years.


Topic Link (if released)
Search Search Notes
CSPs CSPs Notes
Local Search Local Search Notes
Linear and Integer Programming LP/IP Notes
Propositional Logic and SAT Prop Logic and SAT Notes
Classical Planning Classical Planning Notes
Probability Probability Notes
Markov Decision Process MDP Notes
Reinforcement Learning RL Notes
Bayes Nets Bayes Nets Notes
HMMs and Particle Filters HMMs and Particle Filters Notes
Game Theory Game Theory Notes

Full Schedule

Week # Monday Tuesday Wednesday Thursday Friday
1 Lecture: Intro/Agents Lecture: Search Recitation 1
P0 due
2 Lecture: Informed Search
HW1 due
Lecture: Adversarial Search Recitation 2
3 Lecture: CSPs
HW2 due
Lecture: Local Search Recitation 3
4 P1 due Lecture: Optimization
HW3 due
Lecture: Linear/Integer Programming Recitation 4
5 Lecture: Ethics I
HW4 due
EXAM 1 Recitation 5
6 Lecture: Logic Lecture: Classical Planning
P2 due
Recitation 6
7 Lecture: MDPs I
HW5 due
Lecture: MDPs II Recitation 7
P3 1-6 due
8 Lecture: RL I
HW6 due
Lecture: RL II Recitation 8
P3 1-10 due
9 Lecture: Bayes Representation
HW7 due
Lecture: Bayes Independence Recitation 9
10 Lecture: Ethics II
HW8 due
EXAM 2 Recitation 10
11 Lecture: Bayes Inference Lecture: Bayes Sampling
P4 due
Recitation 11
12 Lecture: HMMs
HW9 due
13 Lecture: Particle Filters Lecture: Game Theory I Recitation 13
14 Lecture: Game Theory II
HW10 due
Lecture: Ethics/AMA
P5 due
Recitation 14



Grades will be collected and reported in Canvas. Please let us know if you believe there to be an error the grade reported in Canvas.

Final scores will be composed of:

  • 15% Midterm exams (each)
  • 30% Final exam
  • 20% Programming homework
  • 10% Written homework
  • 5% Online homework
  • 5% Participation

Participation Grades

Participation will be based on the percentage of in-class polling questions answered:

  • 5% for 80% or greater poll participation
  • 3% for 70%
  • 1% for 60%

Correctness of in-class polling responses will not be taken into account for participation grades. Illness, homeworks, and travel are built into this policy. However, if you need to miss more than one lecture, please reach out to the professor to make up missed work.

It is against the course academic integrity policy to answer in-class polls when you are not present in lecture. Violations of this policy will be reported as an academic integrity violation. Information about academic integrity at CMU may be found at https://www.cmu.edu/academic-integrity.

Final Grade

This class is not curved. However, we convert final course scores to letter grades based on grade boundaries that are determined at the end of the semester. What follows is a rough guide to how course grades will be established, not a precise formula — we will fine-tune cutoffs and other details as we see fit after the end of the course. This is meant to help you set expectations and take action if your trajectory in the class does not take you to the grade you are hoping for. So, here's a rough, very rough heuristics about the correlation between final grades and total scores:

  • A: above 90%
  • B: 80-90%
  • C: 70-80%
  • D: 60-70%

This heuristic assumes that the makeup of a student’s grade is not wildly anomalous: exceptionally low overall scores on exams, programming assignments, or written assignments will be treated on a case-by-case basis.

Precise grade cutoffs will not be discussed at any point during or after the semester. For students very close to grade boundaries, instructors may, at their discretion, consider participation in lecture and recitation, exam performance, and overall grade trends when assigning the final grade.

Late Policy

Programming assignments, written homework, and online homework:

  • 6 slip days across all assignment types
  • Use up to two per programming assignment and use up to one per written/online assignment
  • You may use these at your discretion, but they are intended for minor illness and other disruptive events outside of your control, and not for poor time management
  • You are responsible to keep track of your own slip days. Gradescope will not enforce the total number of slip days. We will update our count of slip days a few times per semester.

Aside from this, there will be no extensions on assignments in general. If you think you really really need an extension on a particular assignment, contact the instructor as soon as possible and before the deadline. Please be aware that extensions are entirely discretionary and will be granted only in exceptional circumstances outside of your control (e.g., due to severe illness or major personal/family emergencies, but not for competitions, club-related events or interviews). The instructors will require confirmation from University Health Services or your academic advisor, as appropriate.
Nearly all situations that make you run late on an assignment homework can be avoided with proper planning — often just starting early. Here are some examples:

  • I have so many deadlines this week: you know your deadlines ahead of time — plan accordingly.
  • It's a minute before the deadline and the network is down: you always have multiple submissions -- it's not a good idea to wait for the deadline for your first submission.
  • My computer crashed and I lost everything: Use Dropbox or similar to do real-time backup -- recover your files onto AFS and finish your homework from a cluster machine.
  • My fraternity/sorority/club has that big event that is taking all my time: Schedule your extra-curricular activities around your classes, not vice versa.

Again, you should be keeping track of how many slip days you have used, and ensure that you are both using no more than the allowed slip days per assignment and using no more than 6 slip days in the semester. If you submit an assignment late but do not have enough slip days to use for either reason, one of two things will happen:

  • if you submitted a version of the assignment on time or within your available slip days, we will grade the last valid assignment submission.
  • if you did not submit a version on time, you will receive a 0.

You are encouraged to submit a version of your assignment early. It is not a good idea to wait for the deadline for your first submission.

Collaboration Policy

We encourage you to discuss course content and assignments with your classmates. However, these discussion must be kept at a conceptual level only.

  • You may NOT view, share, or communicate about any artifact that will be submitted as part of an assignment. Example artifacts include, but are not limited to: code, pseudocode, diagrams, and text.
  • If you work on homework problems together, you must erase all artifacts and wait at least 1 hour before writing your responses to ensure that your submission is not too similar from your friends'.
  • You may look at another student's Python error messages and discuss what the error means at a conceptual level. However, you may NOT give specific instructions to fix the error.
  • All work that you present must be your own.
  • Using any external sources of code or algorithms in any way must have approval from the instructor before submitting the work. For example, you must get instructor approval before using an algorithm you found online for implementing a heuristic function in a programming assignment.

Programming Assignment Partners

The only exception to the above collaboration policy is when you share programming code directly with your programming assignment partner.

  • You are allowed to work in groups of at most two on each programming assignment P1-P5, i.e. you and one partner
  • You must specify your parnter when you submit each assignment and each time you submit each assignment (Gradescope requires that)
  • Once you start working with a partner on an assignment, you may not switch to another partner for that assignment
  • You may change partners between assignments. In fact, you are strongly encouraged to change partners occasionally
  • Important: You are responsible for making sure that both you AND your partner understand the work that you submit. If we discover that one partner cannot answer basic questions about the submitted work, both students in the group will be reported for an academic integrity violation.

Violations of these policies will be reported as an academic integrity violation. Information about academic integrity at CMU may be found at https://www.cmu.edu/academic-integrity. Please contact the instructor if you ever have any questions regarding academic integrity or these collaboration policies.

Expectations for Online learning

If for any reason we must switch to online format, we will use the following policies:

We will be using Zoom for lectures, recitations, and exams. If you cannot attend on Zoom for any reason, the recorded lectures will be available within a few hours of classes. If your Internet does not support Zoom consistently for exams or you have other concerns, please let the professors know at least 1 week before an exam and we can try to make an accommodation. The course will also make use of Canvas, Diderot, and Gradescope. If you have trouble accessing these technologies, please let us know ASAP. If you have general concerns about this policy and your ability to access class materials, please let us know ASAP.

If you cannot attend lecture live, must let the professor know ASAP and before class to plan accommodations. As always, the professors are happy to answer questions about lectures via posts on the lecture slides on Diderot or office hours or via email.

Recitations will take place in person or online depending on feasibility. At least one online recitation will be recorded so that remote students who cannot attend any recitation sections can view it. We will re-examine recitation sections and office hours in the weeks we are online.

In this course, being able to see one another helps to facilitate a better learning environment and promote more engaging discussions. Therefore, our default will be to expect students to have their cameras on during lectures and discussions and particularly during proctored exams. However, we also completely understand there may be reasons students would not want to have their cameras on. If you have any concerns about sharing your video during exams, please email us as soon as possible and we can discuss possible adjustments. Note: You may use a background image in your video if you wish; just check in advance that this works with your device(s) and internet bandwidth.

Expectations for In-Person learning

You are responsible for adhering to all CMU policies. If you do not comply, please remember that you will be subject to student conduct proceedings, up to and including removal from CMU. Accordingly, we will be obliged to take other measures for the safety of the whole class.

Accommodations for Students with Disabilities

If you have a disability and have an accommodations letter from the Disability Resources office, we encourage you to discuss your accommodations and needs with us as early in the semester as possible. We will work with you to ensure that accommodations are provided as appropriate. If you suspect that you may have a disability and would benefit from accommodations but are not yet registered with the Office of Disability Resources, we encourage you to visit their website.

Statement of Support for Students’ Health & Well-being

Take care of yourself. Do your best to maintain a healthy lifestyle this semester by eating well, exercising, getting enough sleep, and taking some time to relax. This will help you achieve your goals and cope with stress.
All of us benefit from support during times of struggle. There are many helpful resources available on campus and an important part of the college experience is learning how to ask for help. Asking for support sooner rather than later is almost always helpful.
If you or anyone you know experiences any academic stress, difficult life events, or feelings like anxiety or depression, we strongly encourage you to seek support. Counseling and Psychological Services (CaPS) is here to help: call 412-268-2922 and visit their website at http://www.cmu.edu/counseling/. Consider reaching out to a friend, faculty or family member you trust for help getting connected to the support that can help.
If you have questions about this or your coursework, please let us know. Thank you, and have a great semester.

Statement of Commitment to a Diverse Learning Environment

We must treat every individual with respect. We are diverse in many ways, and this diversity is fundamental to building and maintaining an equitable and inclusive campus community. Diversity can refer to multiple ways that we identify ourselves, including but not limited to race, color, national origin, language, sex, disability, age, sexual orientation, gender identity, religion, creed, ancestry, belief, veteran status, or genetic information. Each of these diverse identities, along with many others not mentioned here, shape the perspectives our students, faculty, and staff bring to our campus. We, at CMU, will work to promote diversity, equity and inclusion not only because diversity fuels excellence and innovation, but because we want to pursue justice. We acknowledge our imperfections while we also fully commit to the work, inside and outside of our classrooms, of building and sustaining a campus community that increasingly embraces these core values.

Each of us is responsible for creating a safer, more inclusive environment.

Unfortunately, incidents of bias or discrimination do occur, whether intentional or unintentional. They contribute to creating an unwelcoming environment for individuals and groups at the university. Therefore, the university encourages anyone who experiences or observes unfair or hostile treatment on the basis of identity to speak out for justice and support, within the moment of the incident or after the incident has passed. Anyone can share these experiences using the following resources:

  • Center for Student Diversity and Inclusion: csdi@andrew.cmu.edu, (412) 268-2150
  • Report-It online anonymous reporting platform: https://www.reportit.net username: tartans password: plaid

All reports will be documented and deliberated to determine if there should be any following actions. Regardless of incident type, the university will use all shared experiences to transform our campus climate to be more equitable and just.